Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
712 conjugacy classes of subgroups; only the 349 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 349 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D59 |
| commutator | C22×C59 | C23×C4 |
| Frattini | C23 | C23×D59 |
| Fitting | C22×C4⋊C4×C59 | C2 |
| socle | C24×C59 | C23 |
| hypercenter | C22×C4⋊C4 | D59 |
| hypocenter | C59 | C2×#382 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C24 ◁ C22×C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #16837267 | C2 | direct (N × H) |
| 10. C2×C4×Dic59 | C4 | semidirect |
| 34. C4×Dic59 | C2×C4 | semidirect |
| 70. C2×C59 | #382 | semidirect |
| 81. C59 | C2×#382 | semidirect |
| 145. C2 | #16837267 | direct (N × H) |