Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
422 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 57 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. #21434999 | C2 | semidirect |
| 2. #21426008 | C2 | semidirect |
| 3. #21425203 | C2 | semidirect |
| 4. #21422114 | C2 | semidirect |
| 5. #21422112 | C2 | semidirect |
| 6. #21422021 | C2 | semidirect |
| 7. C59×#2187 | C2 | semidirect |
| 179. #2187 | D59 | semidirect |
| 211. C59 | #12110 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434999 | 2 |
| #21426008 | 2 |
| #21425203 | 2 |
| #21422114 | 2 |
| #21422112 | 2 |
| #21422021 | 2 |
| C59×#2187 | 2 |
| #12110 | 59 |