Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
568 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 91 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. #21433124 | C2 | semidirect |
| 3. #21422719 | C2 | semidirect |
| 4. #21422719 | C2 | semidirect |
| 5. #21422436 | C2 | semidirect |
| 6. #21421952 | C2 | semidirect |
| 7. C59×#1285 | C2 | semidirect |
| 66. #14273638 | D4 | semidirect |
| 78. #97×C59 | D4 | semidirect |
| 239. #1285 | D59 | semidirect |
| 271. C59 | #9447 | semidirect |
| 317. #97 | D236 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433124 | 2 |
| #21429067 | 2 |
| #21422719 | 2 |
| #21422436 | 2 |
| #21421952 | 2 |
| C59×#1285 | 2 |
| #9447 | 59 |