Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
4614 conjugacy classes of subgroups; only the 491 normal subgroups are shown.
This group has 4614 conjugacy classes of subgroups — too many to draw. Only its 491 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. C2×#16837249 | C2 | semidirect |
| 3. #21422367 | C2 | semidirect |
| 4. #21422336 | C2 | semidirect |
| 5. C59×#1446 | C2 | semidirect |
| 7. C22×#11745689 | C4 | semidirect |
| 50. C22×C4×C59 | #41 | semidirect |
| 55. C22×Dic59 | #41 | semidirect |
| 62. C2×C4×D59 | C22⋊C4 | semidirect |
| 112. #1446 | D59 | semidirect |
| 129. C59 | #13851 | semidirect |
| 176. C22×C4 | #11745689 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11745689 | 2 |
| C2×#16837249 | 2 |
| #21422367 | 2 |
| #21422336 | 2 |
| C59×#1446 | 2 |
| #13851 | 59 |