Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
342 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 59 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. #21426032 | C2 | semidirect |
| 4. #21425364 | C2 | semidirect |
| 5. #21422115 | C2 | semidirect |
| 7. C59×#1323 | C2 | semidirect |
| 161. #1323 | D59 | semidirect |
| 186. C59 | #12169 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435557 | 2 |
| #21426032 | 2 |
| #21426015 | 2 |
| #21425364 | 2 |
| #21422115 | 2 |
| #21422112 | 2 |
| C59×#1323 | 2 |
| #12169 | 59 |