Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
532 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 97 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. #21437230 | C2 | semidirect |
| 2. #21433816 | C2 | semidirect |
| 3. C2×#16837211 | C2 | semidirect |
| 4. #21425824 | C2 | semidirect |
| 5. #21425724 | C2 | semidirect |
| 6. #21422194 | C2 | semidirect |
| 7. C59×#3060 | C2 | semidirect |
| 43. C2×Dic236 | D4 | semidirect |
| 45. C2×D472 | D4 | semidirect |
| 56. C2×C59⋊C16 | D4 | semidirect |
| 58. #14273663 | D4 | semidirect |
| 222. #3060 | D59 | semidirect |
| 259. C59 | #13318 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437230 | 2 |
| #21433816 | 2 |
| C2×#16837211 | 2 |
| #21425824 | 2 |
| #21425724 | 2 |
| #21422194 | 2 |
| C59×#3060 | 2 |
| #13318 | 59 |