Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
500 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 197 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | C22×D59 |
| commutator, socle | C22×C59 | C23×C4 |
| Frattini | C2×C4 | C23×D59 |
| Fitting | C2×C4×C8×C59 | C2 |
| hypercenter | C2×C4×C8 | D59 |
| hypocenter | C59 | #2931 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C2×C8 ◁ C2×C4×C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14273733 | C2 | semidirect |
| 3. #16837481 | C2 | semidirect |
| 4. C8×D236 | C2 | semidirect |
| 5. #16837426 | C2 | semidirect |
| 6. #16837368 | C2 | semidirect |
| 7. C2×C4×C8×C59 | C2 | semidirect |
| 35. C2×C8×C59 | D4 | semidirect |
| 75. C4×C59 | #131 | semidirect |
| 90. C2×C4×C8 | D59 | semidirect |
| 91. C59 | #2931 | semidirect |
| 123. C2×C8 | D236 | semidirect |
| 160. C4 | #14273733 | semidirect |