Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
2528 conjugacy classes of subgroups; only the 685 normal subgroups are shown.
This group has 2528 conjugacy classes of subgroups — too many to draw. Only its 685 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D73 |
| commutator | C22×C73 | C25 |
| Frattini | C22 | C24×D73 |
| Fitting | C22×C4⋊C4×C73 | C2 |
| socle | C24×C73 | C23 |
| hypercenter | C22×C4⋊C4 | D73 |
| hypocenter | C73 | C22×#121 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C24 ◁ C22×C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×D292 | C2 | semidirect |
| 2. C23×D292 | C2 | semidirect |
| 3. C23×C4×D73 | C2 | semidirect |
| 4. C2×#14556566 | C2 | direct (N × H) |
| 5. C22×#11924005 | C2 | semidirect |
| 6. C22×C4⋊C4×C73 | C2 | semidirect |
| 11. C22×D292 | C22 | semidirect |
| 12. C22×D292 | C22 | semidirect |
| 15. C22×C4×D73 | C22 | semidirect |
| 16. #14556566 | C22 | direct (N × H) |
| 17. C2×#11924005 | C22 | semidirect |
| 20. C2×C4⋊C4×C73 | C22 | semidirect |
| 26. C23×D73 | D4 | semidirect |
| 31. C2×D292 | C23 | semidirect |
| 32. C2×D292 | C23 | semidirect |
| 36. C2×C4×D73 | C23 | semidirect |
| 37. #11924005 | C23 | semidirect |
| 40. C22×C4×C73 | D4 | semidirect |
| 43. C4⋊C4×C73 | C23 | semidirect |
| 55. C22×D73 | C2×D4 | semidirect |
| 59. C2×C4×C73 | C2×D4 | semidirect |
| 67. C22×C73 | #121 | semidirect |
| 79. C2×D73 | C22×D4 | semidirect |
| 81. C4×C73 | C22×D4 | semidirect |
| 83. C2×C73 | C2×#121 | semidirect |
| 90. C73 | C22×#121 | semidirect |
| 95. C22×C4⋊C4 | D73 | semidirect |
| 109. C2×C4⋊C4 | C2×D73 | semidirect |
| 129. C22×C4 | D292 | semidirect |
| 132. C4⋊C4 | C22×D73 | semidirect |
| 154. C2×C4 | C2×D292 | semidirect |
| 165. C22 | #14556566 | direct (N × H) |
| 172. C4 | C22×D292 | semidirect |
| 175. C2 | C2×#14556566 | direct (N × H) |