Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
334 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 334 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 |
|---|---|---|
| 4. #21422155 | C2 | semidirect |
| 5. #21422154 | C2 | semidirect |
| 6. #21422153 | C2 | semidirect |
| 7. C59×#1365 | C2 | semidirect |
| 128. #1365 | D59 | semidirect |
| 150. C59 | #11941 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #500×D59 | 2 |
| #21425850 | 2 |
| #21422843 | 2 |
| #21422155 | 2 |
| #21422154 | 2 |
| #21422153 | 2 |
| C59×#1365 | 2 |
| #11941 | 59 |