Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
314 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 314 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. #21436489 | C2 | semidirect |
| 2. #21426320 | C2 | semidirect |
| 3. #21426137 | C2 | semidirect |
| 5. #21422153 | C2 | semidirect |
| 6. #21422061 | C2 | semidirect |
| 7. C59×D4⋊C16 | C2 | semidirect |
| 89. D4×C59 | SD32 | semidirect |
| 136. D4⋊C16 | D59 | semidirect |
| 159. C59 | #12342 | semidirect |
| 232. D4 | #14273672 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21436489 | 2 |
| #21426320 | 2 |
| #21426137 | 2 |
| #21423451 | 2 |
| #21422153 | 2 |
| #21422061 | 2 |
| C59×D4⋊C16 | 2 |
| #12342 | 59 |