Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
1224 conjugacy classes of subgroups; only the 201 normal subgroups are shown.
This group has 1224 conjugacy classes of subgroups — too many to draw. Only its 201 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 | #380×C73 | C2 |
| hypercenter | #380 | D73 |
| hypocenter | C73 | #2847 |
| LCS | G ▷ C23×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ #380 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×C4×D73 | C2 | semidirect |
| 2. C2×#14556566 | C2 | semidirect |
| 3. C2×#14556565 | C2 | semidirect |
| 4. C2×#14556561 | C2 | semidirect |
| 5. #17988465 | C2 | semidirect |
| 6. #17988464 | C2 | semidirect |
| 7. #17988444 | C2 | semidirect |
| 8. #380×C73 | C2 | semidirect |
| 11. C22×D292 | C22 | semidirect |
| 21. C2×C4⋊Dic73 | C22 | semidirect |
| 23. C2×#11924005 | C22 | semidirect |
| 24. C2×#11924005 | C22 | semidirect |
| 25. #14556498 | C22 | semidirect |
| 27. C2×C4⋊C4×C73 | C22 | semidirect |
| 29. #95×C73 | C22 | semidirect |
| 34. C23×D73 | D4 | semidirect |
| 55. C2×C4×D73 | D4 | semidirect |
| 62. C22×C4×C73 | D4 | semidirect |
| 115. C22×C73 | #121 | semidirect |
| 133. C2×D73 | #121 | semidirect |
| 136. C4×C73 | #120 | semidirect |
| 148. C73 | #2847 | semidirect |
| 156. #380 | D73 | semidirect |
| 171. C2×C4⋊C4 | C2×D73 | semidirect |
| 177. #95 | C2×D73 | semidirect |
| 206. C22×C4 | D292 | semidirect |
| 276. C22 | #14556566 | semidirect |
| 286. C4 | #14556561 | semidirect |