Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
668 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 157 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×C22⋊Q8×C59 | C2 |
| hypercenter | C2×C22⋊Q8 | D59 |
| hypocenter | C59 | #2626 |
| LCS | G ▷ C23×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ C2×C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16837337 | C2 | semidirect |
| 3. #16837324 | C2 | semidirect |
| 4. #16837313 | C2 | semidirect |
| 5. #16837274 | C2 | semidirect |
| 6. #16837262 | C2 | semidirect |
| 8. C2×C22⋊Q8×C59 | C2 | semidirect |
| 11. C2×C4⋊Dic59 | C22 | semidirect |
| 12. C2×Dic59⋊C4 | C22 | semidirect |
| 19. C59⋊#95 | C22 | semidirect |
| 20. C59⋊#95 | C22 | semidirect |
| 21. C22×Q8×C59 | C22 | semidirect |
| 24. C2×C4⋊C4×C59 | C22 | semidirect |
| 25. C2×C4⋊C4×C59 | C22 | semidirect |
| 32. C23×D59 | Q8 | semidirect |
| 118. C2×C22⋊Q8 | D59 | semidirect |
| 126. C59 | #2626 | semidirect |
| 128. C22×Q8 | C2×D59 | semidirect |
| 134. C2×C4⋊C4 | C2×D59 | semidirect |
| 135. C2×C4⋊C4 | C2×D59 | semidirect |