Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
396 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 67 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. #21426024 | C2 | semidirect |
| 3. #21425407 | C2 | semidirect |
| 4. #21422108 | C2 | semidirect |
| 5. #21422105 | C2 | semidirect |
| 6. #21422036 | C2 | semidirect |
| 7. C59×#3250 | C2 | semidirect |
| 174. #3250 | D59 | semidirect |
| 207. C59 | #12160 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426024 | 2 |
| #21426007 | 2 |
| #21425407 | 2 |
| #21422108 | 2 |
| #21422105 | 2 |
| #21422036 | 2 |
| C59×#3250 | 2 |
| #12160 | 59 |