Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
362 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 362 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 |
|---|---|---|
| 2. #21426352 | C2 | semidirect |
| 3. #21426142 | C2 | semidirect |
| 4. #21423466 | C2 | semidirect |
| 5. #21422143 | C2 | semidirect |
| 6. #21422058 | C2 | semidirect |
| 7. C59×Q8⋊C16 | C2 | semidirect |
| 93. Q8×C59 | SD32 | semidirect |
| 142. Q8⋊C16 | D59 | semidirect |
| 166. C59 | #12332 | semidirect |
| 237. Q8 | #14273672 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437071 | 2 |
| #21426352 | 2 |
| #21426142 | 2 |
| #21423466 | 2 |
| #21422143 | 2 |
| #21422058 | 2 |
| C59×Q8⋊C16 | 2 |
| #12332 | 59 |