Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
730 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 730 conjugacy classes of subgroups — too many to draw. Only its 117 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. #21433119 | C2 | semidirect |
| 3. #21424085 | C2 | semidirect |
| 4. #21422765 | C2 | semidirect |
| 5. #21422763 | C2 | semidirect |
| 6. #21421999 | C2 | semidirect |
| 7. C59×#1303 | C2 | semidirect |
| 50. C4⋊(C59⋊C8) | D4 | semidirect |
| 61. C4⋊C8×C59 | D4 | semidirect |
| 196. #1303 | D59 | semidirect |
| 222. C59 | #9397 | semidirect |
| 254. C4⋊C8 | D236 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433119 | 2 |
| #21429038 | 2 |
| #21424085 | 2 |
| #21422765 | 2 |
| #21422763 | 2 |
| #21421999 | 2 |
| C59×#1303 | 2 |
| #9397 | 59 |