Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
392 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 173 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 | C4×M16×C73 | C2 |
| hypercenter | C4×M16 | D73 |
| hypocenter | C73 | #2921 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C2×C4 ◁ C4×M16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #17988649 | C2 | semidirect |
| 3. #17988646 | C2 | semidirect |
| 4. #17988610 | C2 | semidirect |
| 6. C4×#11924012 | C2 | semidirect |
| 7. C4×M16×C73 | C2 | semidirect |
| 16. #14556520 | C22 | semidirect |
| 18. #14556502 | C22 | semidirect |
| 19. C4×#10596831 | C22 | semidirect |
| 22. #97×C73 | C22 | semidirect |
| 23. C4×C8×C73 | C22 | semidirect |
| 80. C73 | #2921 | semidirect |
| 87. C4×M16 | D73 | semidirect |
| 101. #97 | C2×D73 | semidirect |
| 103. C4×C8 | C2×D73 | semidirect |