Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
566 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 117 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. #21425851 | C2 | semidirect |
| 3. C2×#16837216 | C2 | semidirect |
| 4. C2×#16837215 | C2 | semidirect |
| 5. C2×#16837214 | C2 | semidirect |
| 6. #108×Dic59 | C2 | semidirect |
| 7. C2×C59×#361 | C2 | semidirect |
| 47. #14273663 | D4 | semidirect |
| 65. #108×C59 | D4 | semidirect |
| 167. Dic59 | #361 | semidirect |
| 173. C2×#361 | D59 | semidirect |
| 199. C59 | #13257 | semidirect |
| 235. #108 | C22⋊D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837777 | 2 |
| #21425851 | 2 |
| C2×#16837216 | 2 |
| C2×#16837215 | 2 |
| C2×#16837214 | 2 |
| #108×Dic59 | 2 |
| C2×C59×#361 | 2 |
| #13257 | 59 |