Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
1812 conjugacy classes of subgroups; only the 223 normal subgroups are shown.
This group has 1812 conjugacy classes of subgroups — too many to draw. Only its 223 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 | C2×#392 |
| 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. C22×D4×D59 | C2 | semidirect |
| 2. C2×C22⋊C4×D59 | C2 | semidirect |
| 3. #16837312 | C2 | semidirect |
| 4. #16837311 | C2 | semidirect |
| 5. #16837310 | C2 | semidirect |
| 6. #95×D59 | C2 | semidirect |
| 7. C59×#392 | C2 | semidirect |
| 9. C22×D236 | C22 | semidirect |
| 10. C22×C22⋊D59 | C22 | semidirect |
| 15. C2×C22⋊Dic59 | C22 | semidirect |
| 16. C2×(C2×D59)⋊C4 | C22 | semidirect |
| 17. C2×(C2×D59)⋊C4 | C22 | semidirect |
| 19. C59⋊#95 | C22 | semidirect |
| 20. C22×D4×C59 | C22 | semidirect |
| 21. C2×C22⋊C4×C59 | C22 | semidirect |
| 22. #95×C59 | C22 | semidirect |
| 28. C23×D59 | D4 | semidirect |
| 45. C2×C4×D59 | D4 | semidirect |
| 54. C23×C59 | C2×D4 | semidirect |
| 67. C22×D59 | C2×D4 | semidirect |
| 72. C2×C4×C59 | C2×D4 | semidirect |
| 76. C2×Dic59 | C2×D4 | semidirect |
| 107. D59 | #392 | direct (N × H) |
| 113. #392 | D59 | direct (N × H) |
| 115. C59 | C2×#392 | semidirect |
| 121. C22×D4 | C2×D59 | semidirect |
| 128. C2×C22⋊C4 | C2×D59 | semidirect |
| 130. #95 | C2×D59 | semidirect |
| 175. C23 | D4×D59 | semidirect |
| 187. C2×C4 | D4×D59 | semidirect |