Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
948 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 948 conjugacy classes of subgroups — too many to draw. Only its 171 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 | C59×#392 | C2 |
| hypercenter | #392 | D59 |
| hypocenter | C59 | #2541 |
| LCS | G ▷ C23×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ #392 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14273723 | C2 | semidirect |
| 2. C2×#14273723 | C2 | semidirect |
| 3. C2×#14273700 | C2 | semidirect |
| 4. C2×#14273699 | C2 | semidirect |
| 5. C2×(C22⋊D59)⋊C4 | C2 | semidirect |
| 6. #16837312 | C2 | semidirect |
| 7. #16837311 | C2 | semidirect |
| 8. #16837310 | C2 | semidirect |
| 9. #16837302 | C2 | semidirect |
| 10. #16837253 | C2 | semidirect |
| 11. C59×#392 | C2 | semidirect |
| 66. C2×C22⋊D59 | D4 | semidirect |
| 87. Dic59⋊C4 | D4 | semidirect |
| 89. C4×Dic59 | D4 | semidirect |
| 177. Dic59 | #121 | semidirect |
| 178. Dic59 | #127 | semidirect |
| 197. #392 | D59 | semidirect |
| 200. C59 | #2541 | semidirect |