Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
1224 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 1224 conjugacy classes of subgroups — too many to draw. Only its 237 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D73 |
| commutator, socle | C23×C73 | C24 |
| Fitting | C24×C4×C73 | C2 |
| hypercenter | C24×C4 | D73 |
| hypocenter | C73 | #2847 |
| LCS | G ▷ C23×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ C24×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14556565 | C2 | semidirect |
| 2. C2×#14556560 | C2 | semidirect |
| 3. #17988466 | C2 | semidirect |
| 4. #17988447 | C2 | semidirect |
| 5. C24×C4×C73 | C2 | semidirect |
| 6. C22×D292 | C22 | semidirect |
| 10. C2×C4⋊Dic73 | C22 | semidirect |
| 12. C2×#11924005 | C22 | semidirect |
| 13. #14556498 | C22 | semidirect |
| 29. C24×C73 | D4 | semidirect |
| 35. C22×C4×C73 | D4 | semidirect |
| 65. C22×C73 | #121 | semidirect |
| 73. C4×C73 | #120 | semidirect |
| 81. C73 | #2847 | semidirect |
| 82. C24×C4 | D73 | semidirect |
| 102. C24 | D292 | semidirect |
| 113. C22×C4 | C22⋊D73 | semidirect |
| 149. C22 | #14556565 | semidirect |
| 155. C4 | #14556560 | semidirect |