Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
180 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | D4×D59 |
| commutator | C4×C59 | C22×C8 |
| Frattini | C42 | C22×D59 |
| Fitting | C59×Q8⋊C8 | C2 |
| socle | C22×C59 | C4×D4 |
| hypercenter | Q8⋊C8 | D59 |
| hypocenter | C59 | C8×SD16 |
| LCS | G ▷ C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C2×C4 ◁ C42 ◁ Q8⋊C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. Q8×C59⋊C8 | C2 | semidirect |
| 4. #16837152 | C2 | semidirect |
| 6. C8×C59⋊C8 | C2 | semidirect |
| 7. C59×Q8⋊C8 | C2 | semidirect |
| 32. #11745671 | C8 | semidirect |
| 43. Q8×C59 | C2×C8 | semidirect |
| 59. C59⋊C8 | C2×C8 | semidirect |
| 60. C59⋊C8 | SD16 | semidirect |
| 82. Q8⋊C8 | D59 | semidirect |
| 85. C59 | C8×SD16 | semidirect |
| 121. Q8 | C8×D59 | semidirect |