Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
172 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | #14273701 |
| commutator | C42×C59 | C23 |
| Frattini | C42 | C22×D59 |
| Fitting | C8×Q8×C59 | C2 |
| socle | C22×C59 | #121 |
| hypercenter | C8×Q8 | D59 |
| hypocenter | C59 | #1666 |
| LCS | G ▷ C42×C59 ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ C8×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16837687 | C2 | semidirect |
| 4. #16837153 | C2 | semidirect |
| 5. #16837149 | C2 | semidirect |
| 7. C8×Q8×C59 | C2 | semidirect |
| 44. Q8×C59 | SD16 | semidirect |
| 60. C8×C59 | SD16 | semidirect |
| 83. C8×Q8 | D59 | semidirect |
| 87. C59 | #1666 | semidirect |
| 126. Q8 | #11745660 | semidirect |
| 142. C8 | #11745671 | semidirect |