Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
556 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 139 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. #21425674 | C2 | semidirect |
| 2. #21425270 | C2 | semidirect |
| 3. #21425266 | C2 | semidirect |
| 4. #21425071 | C2 | semidirect |
| 7. #21424336 | C2 | semidirect |
| 8. #21424334 | C2 | semidirect |
| 56. C4⋊Q8×C59 | Q8 | semidirect |
| 57. #127×C59 | Q8 | semidirect |
| 58. #124×C59 | Q8 | semidirect |
| 59. #124×C59 | Q8 | semidirect |
| 201. C59 | #32704 | semidirect |
| 212. C4⋊Q8 | Dic118 | semidirect |
| 213. #127 | Dic118 | semidirect |
| 215. #124 | Dic118 | semidirect |
| 216. #124 | Dic118 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21425674 | 2 |
| #21425270 | 2 |
| #21425266 | 2 |
| #21425071 | 2 |
| #21424925 | 2 |
| #21424480 | 2 |
| #21424336 | 2 |
| #21424334 | 2 |
| C59×#1884 | 2 |
| #32704 | 59 |