Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
508 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 95 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. #21429107 | C2 | semidirect |
| 4. #21421975 | C2 | semidirect |
| 5. #21421964 | C2 | semidirect |
| 6. #21421942 | C2 | semidirect |
| 54. C22×D4×C59 | Q8 | semidirect |
| 62. C2×C4⋊C4×C59 | Q8 | semidirect |
| 256. C59 | #10374 | semidirect |
| 259. C22×D4 | Dic118 | semidirect |
| 277. C2×C4⋊C4 | Dic118 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21429107 | 2 |
| #21424933 | 2 |
| #21422664 | 2 |
| #21421975 | 2 |
| #21421964 | 2 |
| #21421942 | 2 |
| C2×C59×#327 | 2 |
| #10374 | 59 |