Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
324 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 99 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. C2×#16837231 | C2 | semidirect |
| 4. #21423978 | C2 | semidirect |
| 5. #21422192 | C2 | semidirect |
| 6. #21422173 | C2 | semidirect |
| 16. #16837206 | C4 | semidirect |
| 17. #16837206 | C4 | semidirect |
| 18. #16837203 | C4 | semidirect |
| 19. #16837203 | C4 | semidirect |
| 178. C59 | #13134 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837231 | 2 |
| #21425803 | 2 |
| #21424985 | 2 |
| #21423978 | 2 |
| #21422192 | 2 |
| #21422173 | 2 |
| C2×C59×#359 | 2 |
| #13134 | 59 |