Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
684 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 85 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. #21435099 | C2 | semidirect |
| 2. #21434470 | C2 | semidirect |
| 3. #21422810 | C2 | semidirect |
| 4. #21422694 | C2 | semidirect |
| 5. #21422607 | C2 | semidirect |
| 6. #21421989 | C2 | semidirect |
| 34. #14273727 | D4 | semidirect |
| 35. #14273727 | D4 | semidirect |
| 43. C4⋊(C59⋊C8) | D4 | semidirect |
| 52. #14273638 | D4 | semidirect |
| 231. C59 | #10096 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435099 | 2 |
| #21434470 | 2 |
| #21422810 | 2 |
| #21422694 | 2 |
| #21422607 | 2 |
| #21421989 | 2 |
| C59×#2657 | 2 |
| #10096 | 59 |