Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
836 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 836 conjugacy classes of subgroups — too many to draw. Only its 173 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 | #2432 |
| 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. C2×#14273716 | C2 | semidirect |
| 3. C2×#14273703 | C2 | semidirect |
| 4. #16837319 | C2 | semidirect |
| 5. #16837309 | C2 | semidirect |
| 6. #16837304 | C2 | semidirect |
| 7. #16837273 | C2 | semidirect |
| 8. C4×(C2×D59)⋊C4 | C2 | semidirect |
| 9. C2×C4⋊Q8×C59 | C2 | semidirect |
| 94. C2×C4×C59 | #41 | semidirect |
| 138. C2×C4⋊Q8 | D59 | semidirect |
| 146. C59 | #2432 | semidirect |
| 241. C2×C4 | #11745689 | semidirect |