Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
408 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 113 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. C2×#16837224 | C2 | semidirect |
| 4. #21424832 | C2 | semidirect |
| 5. #21422205 | C2 | semidirect |
| 6. #21422175 | C2 | semidirect |
| 18. #16837206 | C4 | semidirect |
| 19. #16837203 | C4 | semidirect |
| 73. Q16×C59 | C4⋊C4 | semidirect |
| 77. D8×C59 | C4⋊C4 | semidirect |
| 180. C59 | #12955 | semidirect |
| 229. Q16 | Dic59⋊C4 | semidirect |
| 233. D8 | Dic59⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837524 | 2 |
| C2×#16837224 | 2 |
| #21425808 | 2 |
| #21424832 | 2 |
| #21422205 | 2 |
| #21422175 | 2 |
| C2×C59×#360 | 2 |
| #12955 | 59 |