Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
378 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 93 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. #21434636 | C2 | semidirect |
| 5. #21422206 | C2 | semidirect |
| 6. #21422184 | C2 | semidirect |
| 7. C59×#1382 | C2 | semidirect |
| 31. C2×D472 | Q8 | semidirect |
| 158. #1382 | D59 | semidirect |
| 183. C59 | #13369 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434636 | 2 |
| #21425811 | 2 |
| C2×#16837204 | 2 |
| #21425004 | 2 |
| #21422206 | 2 |
| #21422184 | 2 |
| C59×#1382 | 2 |
| #13369 | 59 |