Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
402 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 183 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 | C8×Q8×C59 | C2 |
| hypercenter | C8×Q8 | D59 |
| hypocenter | C59 | #2971 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C2×C4 ◁ C8×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. Q8×C59⋊C8 | C2 | semidirect |
| 3. #16837481 | C2 | semidirect |
| 4. #16837479 | C2 | semidirect |
| 5. #16837458 | C2 | semidirect |
| 6. C4×#11745659 | C2 | semidirect |
| 7. C8×Q8×C59 | C2 | semidirect |
| 44. Q8×C59 | M16 | semidirect |
| 57. C8×C59 | #41 | semidirect |
| 59. C59⋊C8 | #41 | semidirect |
| 78. C8×Q8 | D59 | semidirect |
| 83. C59 | #2971 | semidirect |
| 120. Q8 | #11745659 | semidirect |
| 135. C8 | #11745689 | semidirect |