Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
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×D59 |
| commutator, socle | C22×C59 | C23×C4 |
| Fitting | C4×M16×C59 | C2 |
| hypercenter | C4×M16 | D59 |
| hypocenter | C59 | #2921 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C2×C4 ◁ C4×M16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16837464 | C2 | semidirect |
| 3. #16837461 | C2 | semidirect |
| 4. #16837425 | C2 | semidirect |
| 6. C4×#11745664 | C2 | semidirect |
| 7. C4×M16×C59 | C2 | semidirect |
| 16. Dic59⋊C8 | C22 | semidirect |
| 18. #14273638 | C22 | semidirect |
| 19. C4×C59⋊C8 | C22 | semidirect |
| 22. #97×C59 | C22 | semidirect |
| 23. C4×C8×C59 | C22 | semidirect |
| 86. C4×M16 | D59 | semidirect |
| 87. C59 | #2921 | semidirect |
| 101. #97 | C2×D59 | semidirect |
| 103. C4×C8 | C2×D59 | semidirect |