Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
372 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 71 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. #21426332 | C2 | semidirect |
| 2. #21426243 | C2 | semidirect |
| 3. #21423609 | C2 | semidirect |
| 4. #21422139 | C2 | semidirect |
| 5. #21422063 | C2 | semidirect |
| 6. #21422054 | C2 | semidirect |
| 8. #16837807 | C22 | semidirect |
| 11. C4⋊(C59⋊C16) | C22 | semidirect |
| 15. #16837178 | C22 | semidirect |
| 16. #16837153 | C22 | semidirect |
| 85. D8×C59 | SD16 | semidirect |
| 193. C59 | #12378 | semidirect |
| 253. D8 | #11745670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426332 | 2 |
| #21426243 | 2 |
| #21423609 | 2 |
| #21422139 | 2 |
| #21422063 | 2 |
| #21422054 | 2 |
| C59×#3273 | 2 |
| #12378 | 59 |