Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
612 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 115 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. #21425041 | C2 | semidirect |
| 3. #21422608 | C2 | semidirect |
| 5. #21421988 | C2 | semidirect |
| 6. #21421953 | C2 | semidirect |
| 24. C59×#474 | C4 | semidirect |
| 25. C59×#461 | C4 | semidirect |
| 50. C4⋊Q8×C59 | C2×C4 | semidirect |
| 51. C4⋊Q8×C59 | C2×C4 | semidirect |
| 66. C4⋊C8×C59 | C2×C4 | semidirect |
| 197. #474 | Dic59 | semidirect |
| 198. #461 | Dic59 | semidirect |
| 214. C59 | #9323 | semidirect |
| 220. C4⋊Q8 | C2×Dic59 | semidirect |
| 221. C4⋊Q8 | C2×Dic59 | semidirect |
| 243. C4⋊C8 | C2×Dic59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426457 | 2 |
| #21425041 | 2 |
| #21422608 | 2 |
| #21422539 | 2 |
| #21421988 | 2 |
| #21421953 | 2 |
| C59×#3110 | 2 |
| #9323 | 59 |