Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
454 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 79 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. #21425781 | C2 | semidirect |
| 2. #21425761 | C2 | semidirect |
| 3. #21422253 | C2 | semidirect |
| 8. #16837199 | C22 | semidirect |
| 9. #16837197 | C22 | semidirect |
| 14. C2×#127×C59 | C4 | semidirect |
| 15. C59×#496 | C4 | semidirect |
| 19. C4×M16×C59 | C4 | semidirect |
| 164. C2×#127 | Dic59 | semidirect |
| 165. #496 | Dic59 | semidirect |
| 171. C4×M16 | Dic59 | semidirect |
| 176. C59 | #13579 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21425781 | 2 |
| #21425761 | 2 |
| #21422253 | 2 |
| C59×#3151 | 2 |
| #13579 | 59 |