Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
628 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 628 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 3. #99×Dic59 | C2 | semidirect |
| 4. #21422220 | C2 | semidirect |
| 6. C2×D4×Dic59 | C4 | semidirect |
| 9. #16837305 | C4 | semidirect |
| 13. #16837268 | C4 | semidirect |
| 15. #16837248 | C4 | semidirect |
| 16. #16837195 | C4 | semidirect |
| 20. C59×#353 | C4 | semidirect |
| 36. #14273642 | C2×C4 | semidirect |
| 50. #99×C59 | C2×C4 | semidirect |
| 62. C2×D4×C59 | C42 | semidirect |
| 83. C42×C59 | C42 | semidirect |
| 195. #353 | Dic59 | semidirect |
| 197. C59 | #12628 | semidirect |
| 223. #99 | C2×Dic59 | semidirect |
| 239. C2×D4 | C4×Dic59 | semidirect |
| 271. C42 | C4×Dic59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426822 | 2 |
| C2×#16837195 | 2 |
| #99×Dic59 | 2 |
| #21422220 | 2 |
| C2×C59×#353 | 2 |
| #12628 | 59 |