Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
322 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 4. #21422079 | C2 | semidirect |
| 5. #21422078 | C2 | semidirect |
| 6. #21422077 | C2 | semidirect |
| 7. C59×#1338 | C2 | semidirect |
| 146. #1338 | D59 | semidirect |
| 170. C59 | #11612 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433027 | 2 |
| #21425850 | 2 |
| #346×D59 | 2 |
| #21422079 | 2 |
| #21422078 | 2 |
| #21422077 | 2 |
| C59×#1338 | 2 |
| #11612 | 59 |