Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
394 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 394 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 |
|---|---|---|
| 2. C2×#16837224 | C2 | semidirect |
| 5. #21424887 | C2 | semidirect |
| 6. #21422183 | C2 | semidirect |
| 7. C59×#1383 | C2 | semidirect |
| 21. #16837208 | C4 | semidirect |
| 44. C2×C59⋊C16 | C2×C4 | semidirect |
| 59. #108×C59 | C2×C4 | semidirect |
| 152. #1383 | D59 | semidirect |
| 177. C59 | #12949 | semidirect |
| 207. #108 | C4×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432979 | 2 |
| C2×#16837224 | 2 |
| #21425846 | 2 |
| #21425823 | 2 |
| #21424887 | 2 |
| #21422183 | 2 |
| C59×#1383 | 2 |
| #12949 | 59 |