Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
446 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 75 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. #21430266 | C2 | semidirect |
| 4. #21422001 | C2 | semidirect |
| 5. #21421982 | C2 | semidirect |
| 6. #21421950 | C2 | semidirect |
| 52. C22×D4×C59 | Q8 | semidirect |
| 59. C2×C4⋊C4×C59 | Q8 | semidirect |
| 236. C59 | #10382 | semidirect |
| 239. C22×D4 | Dic118 | semidirect |
| 251. C2×C4⋊C4 | Dic118 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21430266 | 2 |
| #21424933 | 2 |
| #21422625 | 2 |
| #21422001 | 2 |
| #21421982 | 2 |
| #21421950 | 2 |
| C59×#1507 | 2 |
| #10382 | 59 |