Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
240 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 240 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. #21426146 | C2 | semidirect |
| 4. #21422166 | C2 | semidirect |
| 5. #21422144 | C2 | semidirect |
| 7. C8×Q16×C59 | C2 | semidirect |
| 112. C8×Q16 | D59 | semidirect |
| 135. C59 | #12429 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426146 | 2 |
| #21426136 | 2 |
| #21423702 | 2 |
| #21422166 | 2 |
| #21422144 | 2 |
| #21422141 | 2 |
| C8×Q16×C59 | 2 |
| #12429 | 59 |