Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
732 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 732 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 |
|---|---|---|
| 1. #21427270 | C2 | semidirect |
| 2. C2×#16837197 | C2 | semidirect |
| 4. #21422215 | C2 | semidirect |
| 19. C59×#455 | C4 | semidirect |
| 74. C2×Q8×C59 | C22⋊C4 | semidirect |
| 108. C42×C59 | C22⋊C4 | semidirect |
| 213. #455 | Dic59 | semidirect |
| 225. C59 | #13050 | semidirect |
| 278. C2×Q8 | C22⋊Dic59 | semidirect |
| 321. C42 | C22⋊Dic59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21427270 | 2 |
| C2×#16837197 | 2 |
| #21424044 | 2 |
| #21422215 | 2 |
| C2×C59×#455 | 2 |
| #13050 | 59 |