Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
216 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 216 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. #21426411 | C2 | semidirect |
| 2. #21426346 | C2 | semidirect |
| 3. #21425978 | C2 | semidirect |
| 4. #21422287 | C2 | semidirect |
| 5. C59×#1422 | C2 | semidirect |
| 22. Dic472 | D4 | semidirect |
| 27. D944 | D4 | semidirect |
| 80. #1422 | D59 | semidirect |
| 97. C59 | #13692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426411 | 2 |
| #21426346 | 2 |
| #21425978 | 2 |
| #21422287 | 2 |
| C59×#1422 | 2 |
| #13692 | 59 |