Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
434 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 55 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. #21429586 | C2 | semidirect |
| 3. #21423133 | C2 | semidirect |
| 4. #21422124 | C2 | semidirect |
| 5. #21422102 | C2 | semidirect |
| 6. #21422027 | C2 | semidirect |
| 7. C59×#1610 | C2 | semidirect |
| 191. #1610 | D59 | semidirect |
| 221. C59 | #12196 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21429586 | 2 |
| #21425138 | 2 |
| #21423133 | 2 |
| #21422124 | 2 |
| #21422102 | 2 |
| #21422027 | 2 |
| C59×#1610 | 2 |
| #12196 | 59 |