Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
498 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 105 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. #21432949 | C2 | semidirect |
| 3. #21425832 | C2 | semidirect |
| 4. #21425811 | C2 | semidirect |
| 5. #21422197 | C2 | semidirect |
| 6. #21422182 | C2 | semidirect |
| 7. C59×#1976 | C2 | semidirect |
| 12. C2×#14273670 | C4 | semidirect |
| 13. C2×#14273668 | C4 | semidirect |
| 45. C2×C59⋊C16 | C2×C4 | semidirect |
| 54. C2×Q16×C59 | C2×C4 | semidirect |
| 56. C2×D8×C59 | C2×C4 | semidirect |
| 172. #1976 | D59 | semidirect |
| 200. C59 | #13033 | semidirect |
| 207. C2×Q16 | C4×D59 | semidirect |
| 215. C2×D8 | C4×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837837 | 2 |
| #21432949 | 2 |
| #21425832 | 2 |
| #21425811 | 2 |
| #21422197 | 2 |
| #21422182 | 2 |
| C59×#1976 | 2 |
| #13033 | 59 |