Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
840 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 205 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 | C23×Q8×C59 | C2 |
| hypercenter | C23×Q8 | D59 |
| hypocenter | C59 | #2409 |
| LCS | G ▷ C23×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ C23×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14273703 | C2 | semidirect |
| 3. #16837321 | C2 | semidirect |
| 4. #16837313 | C2 | semidirect |
| 5. #16837309 | C2 | semidirect |
| 7. #16837275 | C2 | semidirect |
| 8. #16837262 | C2 | semidirect |
| 9. C23×Q8×C59 | C2 | semidirect |
| 38. C2×Q8×C59 | D4 | semidirect |
| 48. C2×C22⋊D59 | Q8 | semidirect |
| 73. C22×D59 | C2×Q8 | semidirect |
| 95. C2×Dic59 | C2×Q8 | semidirect |
| 101. C22×C59 | C22⋊Q8 | semidirect |
| 127. C23×Q8 | D59 | semidirect |
| 136. C59 | #2409 | semidirect |
| 165. C2×Q8 | C22⋊D59 | semidirect |
| 233. C22 | #14273703 | semidirect |