Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
720 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 720 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 |
|---|---|---|
| 2. C4×#14273642 | C2 | semidirect |
| 3. #21422221 | C2 | semidirect |
| 7. #16837195 | C4 | direct (N × H) |
| 11. C2×C4×D4×C59 | C4 | semidirect |
| 14. C59×#390 | C4 | semidirect |
| 16. C59×#384 | C4 | semidirect |
| 17. C43×C59 | C4 | semidirect |
| 21. #14273642 | C2×C4 | semidirect |
| 57. C2×D4×C59 | C42 | semidirect |
| 87. C42×C59 | C42 | semidirect |
| 157. C4×C59 | #353 | semidirect |
| 172. C2×C4×D4 | Dic59 | semidirect |
| 176. #390 | Dic59 | semidirect |
| 178. #384 | Dic59 | semidirect |
| 180. C43 | Dic59 | semidirect |
| 183. C59 | C4×#353 | semidirect |
| 223. C2×D4 | C4×Dic59 | semidirect |
| 256. C42 | C4×Dic59 | semidirect |
| 323. C4 | #16837195 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837195 | 2 |
| C4×#14273642 | 2 |
| #21422221 | 2 |
| C4×#127×C59 | 2 |
| C4×#353 | 59 |