Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
390 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 390 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 |
|---|---|---|
| 2. #21424267 | C2 | semidirect |
| 3. #21422885 | C2 | semidirect |
| 6. #21421934 | C2 | semidirect |
| 7. C59×#1299 | C2 | semidirect |
| 126. D236 | #108 | semidirect |
| 168. #1299 | D59 | semidirect |
| 196. C59 | #8898 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433222 | 2 |
| #21424267 | 2 |
| #21422885 | 2 |
| #21422536 | 2 |
| #21422476 | 2 |
| #21421934 | 2 |
| C59×#1299 | 2 |
| #8898 | 59 |