Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
726 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 253 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×C22⋊D59 |
| commutator | C4×C59 | C23×C4 |
| Frattini | C2×C4 | C23×D59 |
| Fitting | C59×#520 | C2 |
| socle | C22×C59 | C22×D4 |
| hypercenter | #520 | D59 |
| hypocenter | C59 | #2898 |
| LCS | G ▷ C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ C2×#41 ◁ #520 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#14273734 | C2 | semidirect |
| 3. #16837410 | C2 | semidirect |
| 4. #16837401 | C2 | semidirect |
| 5. #16837396 | C2 | semidirect |
| 6. C2×#14273650 | C2 | semidirect |
| 7. C59×#520 | C2 | semidirect |
| 9. #14273774 | C4 | semidirect |
| 38. #11745685 | C2×C4 | semidirect |
| 43. C2×Dic118 | C2×C4 | semidirect |
| 97. #520 | D59 | semidirect |
| 102. C59 | #2898 | semidirect |