Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
400 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 113 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. #21425884 | C2 | semidirect |
| 3. C2×#16837227 | C2 | semidirect |
| 6. #21422193 | C2 | semidirect |
| 7. C59×#1387 | C2 | semidirect |
| 21. #16837187 | C4 | semidirect |
| 43. C2×C59⋊C16 | C2×C4 | semidirect |
| 57. M32×C59 | C2×C4 | semidirect |
| 157. #1387 | D59 | semidirect |
| 183. C59 | #12925 | semidirect |
| 203. M32 | C4×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432692 | 2 |
| #21425884 | 2 |
| C2×#16837227 | 2 |
| C2×#16837187 | 2 |
| #21424157 | 2 |
| #21422193 | 2 |
| C59×#1387 | 2 |
| #12925 | 59 |