Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D59 |
| commutator, socle | C23×C59 | C24 |
| Fitting | C2×C4⋊Q8×C59 | C2 |
| hypercenter | C2×C4⋊Q8 | D59 |
| hypocenter | C59 | #2731 |
| LCS | G ▷ C23×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ C2×C4⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16837324 | C2 | semidirect |
| 4. #16837313 | C2 | semidirect |
| 5. #16837309 | C2 | semidirect |
| 6. #16837293 | C2 | semidirect |
| 7. #16837292 | C2 | semidirect |
| 8. #16837283 | C2 | semidirect |
| 9. C2×C4⋊Q8×C59 | C2 | semidirect |
| 126. C2×C4⋊Q8 | D59 | semidirect |
| 135. C59 | #2731 | semidirect |