Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
1620 conjugacy classes of subgroups; only the 573 normal subgroups are shown.
This group has 1620 conjugacy classes of subgroups — too many to draw. Only its 573 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D59 |
| commutator | C22×C59 | C25 |
| Frattini | C22 | C24×D59 |
| Fitting | C22×#41×C59 | C2 |
| socle | C23×C59 | C24 |
| hypercenter | C22×#41 | D59 |
| hypocenter | C59 | C2×#548 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ C22×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×Q8×D59 | C2 | semidirect |
| 2. #16838059 | C2 | direct (N × H) |
| 3. C2×#14273714 | C2 | semidirect |
| 4. C2×#14273706 | C2 | semidirect |
| 5. C2×#14273698 | C2 | semidirect |
| 6. C2×Q8×Dic59 | C2 | semidirect |
| 7. C2×C4×C22⋊D59 | C2 | semidirect |
| 8. C22×#41×C59 | C2 | semidirect |
| 11. C2×Q8×D59 | C22 | semidirect |
| 14. #14273714 | C22 | semidirect |
| 15. #14273706 | C22 | semidirect |
| 16. #14273698 | C22 | semidirect |
| 17. Q8×Dic59 | C22 | semidirect |
| 18. C4×C22⋊D59 | C22 | semidirect |
| 26. C2×#41×C59 | C22 | semidirect |
| 33. C2×Q8×C59 | D4 | semidirect |
| 64. C22×D59 | #41 | semidirect |
| 66. Q8×C59 | C2×D4 | semidirect |
| 93. C2×D59 | C2×#41 | semidirect |
| 101. C2×C59 | #548 | semidirect |
| 106. C22×#41 | D59 | semidirect |
| 114. C59 | C2×#548 | semidirect |
| 116. C2×#41 | C2×D59 | semidirect |
| 142. C2×Q8 | C22⋊D59 | semidirect |
| 173. Q8 | C2×C22⋊D59 | semidirect |
| 207. C2 | #16838059 | direct (N × H) |