Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
388 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | D4×D73 |
| commutator | C4×C73 | C2×C42 |
| Frattini | C22×C4 | C22×D73 |
| Fitting | #340×C73 | C2 |
| socle | C23×C73 | C2×D4 |
| hypercenter | #340 | D73 |
| hypocenter | C73 | #1762 |
| LCS | G ▷ C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ #340 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C2×#14556501 | C2 | semidirect |
| 5. C4⋊C4×Dic73 | C2 | semidirect |
| 6. #17988349 | C2 | semidirect |
| 7. #340×C73 | C2 | semidirect |
| 12. #14556553 | C4 | semidirect |
| 17. #14556513 | C4 | semidirect |
| 18. #14556511 | C4 | semidirect |
| 39. C2×#10596831 | C2×C4 | semidirect |
| 41. C4⋊Dic73 | C2×C4 | semidirect |
| 51. C2×C8×C73 | C2×C4 | semidirect |
| 55. C4⋊C4×C73 | C2×C4 | semidirect |
| 88. D292 | C42 | semidirect |
| 124. C73 | #1762 | semidirect |
| 131. #340 | D73 | semidirect |
| 169. C2×C8 | C4×D73 | semidirect |
| 175. C4⋊C4 | C4×D73 | semidirect |