Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
314 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 75 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. #21426321 | C2 | semidirect |
| 2. #21426136 | C2 | semidirect |
| 4. #21422154 | C2 | semidirect |
| 5. #21422060 | C2 | semidirect |
| 6. D4⋊(C59⋊C16) | C2 | semidirect |
| 7. C59×#3338 | C2 | semidirect |
| 92. D4×C59 | SD32 | semidirect |
| 130. #3338 | D59 | semidirect |
| 159. C59 | #12342 | semidirect |
| 232. D4 | #14273670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426321 | 2 |
| #21426136 | 2 |
| #21423451 | 2 |
| #21422154 | 2 |
| #21422060 | 2 |
| D4⋊(C59⋊C16) | 2 |
| C59×#3338 | 2 |
| #12342 | 59 |