Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
432 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 69 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. #21424178 | C2 | semidirect |
| 3. #21422409 | C2 | semidirect |
| 4. #21422124 | C2 | semidirect |
| 5. #21422122 | C2 | semidirect |
| 6. #21422099 | C2 | semidirect |
| 7. C59×#1345 | C2 | semidirect |
| 196. #1345 | D59 | semidirect |
| 223. C59 | #11847 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21429657 | 2 |
| #21424178 | 2 |
| #21422409 | 2 |
| #21422124 | 2 |
| #21422122 | 2 |
| #21422099 | 2 |
| C59×#1345 | 2 |
| #11847 | 59 |