Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
452 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 177 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D73 |
| commutator, socle | C22×C73 | C23×C4 |
| Fitting | #431×C73 | C2 |
| hypercenter | #431 | D73 |
| hypocenter | C73 | #2975 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C2×C4 ◁ #431 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #17988666 | C2 | semidirect |
| 3. #17988664 | C2 | semidirect |
| 4. #17988640 | C2 | semidirect |
| 5. #17988549 | C2 | semidirect |
| 6. #431×C73 | C2 | semidirect |
| 9. C2×#11924011 | C22 | semidirect |
| 16. C4⋊#10596831 | C22 | semidirect |
| 18. #14556503 | C22 | semidirect |
| 19. C4×#10596831 | C22 | semidirect |
| 21. C4⋊C8×C73 | C22 | semidirect |
| 23. C4×C8×C73 | C22 | semidirect |
| 53. C2×C4×C73 | M16 | semidirect |
| 89. C73 | #2975 | semidirect |
| 94. #431 | D73 | semidirect |
| 107. C4⋊C8 | C2×D73 | semidirect |
| 112. C4×C8 | C2×D73 | semidirect |
| 148. C2×C4 | #11924011 | semidirect |