Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
184 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #21425977 | C2 | semidirect |
| 2. #21422300 | C2 | semidirect |
| 3. #21422280 | C2 | semidirect |
| 4. #21422229 | C2 | semidirect |
| 12. C59×Q64 | C4 | semidirect |
| 13. C59×SD64 | C4 | semidirect |
| 14. C59×D32 | C4 | semidirect |
| 69. Q64 | Dic59 | semidirect |
| 70. SD64 | Dic59 | semidirect |
| 71. D32 | Dic59 | semidirect |
| 77. C59 | #13656 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21425977 | 2 |
| #21422300 | 2 |
| #21422280 | 2 |
| #21422229 | 2 |
| C59×#2262 | 2 |
| #13656 | 59 |