Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
338 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 63 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. #21426279 | C2 | semidirect |
| 2. #21426274 | C2 | semidirect |
| 3. #21425536 | C2 | semidirect |
| 4. #21422111 | C2 | semidirect |
| 5. #21422111 | C2 | semidirect |
| 6. #21422022 | C2 | semidirect |
| 8. C2×#14273661 | C22 | semidirect |
| 14. C22⋊(C59⋊C16) | C22 | semidirect |
| 15. C22⋊(C59⋊C16) | C22 | semidirect |
| 17. #16837167 | C22 | semidirect |
| 190. C59 | #12284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426279 | 2 |
| #21426274 | 2 |
| #21425536 | 2 |
| #21422111 | 2 |
| #21422022 | 2 |
| C59×#3199 | 2 |
| #12284 | 59 |