Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
424 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
| 5. #21424881 | C2 | semidirect |
| 6. #21422192 | C2 | semidirect |
| 7. C59×#1379 | C2 | semidirect |
| 20. #16837216 | C4 | semidirect |
| 42. #14273663 | C2×C4 | semidirect |
| 56. M32×C59 | C2×C4 | semidirect |
| 160. #1379 | D59 | semidirect |
| 185. C59 | #12940 | semidirect |
| 205. M32 | C4×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432949 | 2 |
| #21425884 | 2 |
| C2×#16837216 | 2 |
| C2×#16837204 | 2 |
| #21424881 | 2 |
| #21422192 | 2 |
| C59×#1379 | 2 |
| #12940 | 59 |