Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
888 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 888 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. #21427161 | C2 | semidirect |
| 2. C2×#16837195 | C2 | semidirect |
| 3. #21424044 | C2 | semidirect |
| 4. #21422215 | C2 | semidirect |
| 19. C59×#453 | C4 | semidirect |
| 42. H(5,𝔽2)×C59 | C2×C4 | semidirect |
| 61. #100×C59 | C2×C4 | semidirect |
| 92. C2×D4×C59 | C22⋊C4 | semidirect |
| 113. C42×C59 | C22⋊C4 | semidirect |
| 230. #453 | Dic59 | semidirect |
| 241. C59 | #13047 | semidirect |
| 245. H(5,𝔽2) | C2×Dic59 | semidirect |
| 276. #100 | C2×Dic59 | semidirect |
| 312. C2×D4 | C22⋊Dic59 | semidirect |
| 343. C42 | C22⋊Dic59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21427161 | 2 |
| C2×#16837195 | 2 |
| #21424044 | 2 |
| #21422215 | 2 |
| C2×C59×#453 | 2 |
| #13047 | 59 |