Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 53 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. #21426408 | C2 | semidirect |
| 2. #21426344 | C2 | semidirect |
| 3. #21425977 | C2 | semidirect |
| 4. #21422293 | C2 | semidirect |
| 5. #21422287 | C2 | semidirect |
| 6. #21422286 | C2 | semidirect |
| 7. C59×#2263 | C2 | semidirect |
| 37. Q32×C59 | D4 | semidirect |
| 41. D16×C59 | D4 | semidirect |
| 96. #2263 | D59 | semidirect |
| 122. C59 | #13692 | semidirect |
| 129. Q32 | C22⋊D59 | semidirect |
| 136. D16 | C22⋊D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426408 | 2 |
| #21426344 | 2 |
| #21425977 | 2 |
| #21422293 | 2 |
| #21422287 | 2 |
| #21422286 | 2 |
| C59×#2263 | 2 |
| #13692 | 59 |