Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
636 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 636 conjugacy classes of subgroups — too many to draw. Only its 143 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. #21437246 | C2 | semidirect |
| 2. #21435901 | C2 | semidirect |
| 3. #21426349 | C2 | semidirect |
| 4. #21426222 | C2 | semidirect |
| 5. #21426177 | C2 | semidirect |
| 6. #21426075 | C2 | semidirect |
| 7. #21425934 | C2 | semidirect |
| 8. C59×#2178 | C2 | semidirect |
| 141. #2178 | D59 | semidirect |
| 169. C59 | #33860 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437246 | 2 |
| #21435901 | 2 |
| #21426349 | 2 |
| #21426222 | 2 |
| #21426177 | 2 |
| #21426075 | 2 |
| #21425934 | 2 |
| C59×#2178 | 2 |
| #33860 | 59 |