Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
926 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 926 conjugacy classes of subgroups — too many to draw. Only its 171 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. #21435294 | C2 | semidirect |
| 3. #21423407 | C2 | semidirect |
| 4. #21423394 | C2 | semidirect |
| 5. #21422731 | C2 | semidirect |
| 6. #21422711 | C2 | semidirect |
| 7. C59×#3550 | C2 | semidirect |
| 171. #3550 | D59 | semidirect |
| 207. C59 | #19054 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435294 | 2 |
| #21434541 | 2 |
| #21423407 | 2 |
| #21423394 | 2 |
| #21422731 | 2 |
| #21422711 | 2 |
| C59×#3550 | 2 |
| #19054 | 59 |