Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
492 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 109 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. #21426844 | C2 | semidirect |
| 4. #21422776 | C2 | semidirect |
| 6. #21421955 | C2 | semidirect |
| 7. C59×#1274 | C2 | semidirect |
| 10. #16837775 | C4 | semidirect |
| 11. #16837753 | C4 | semidirect |
| 92. C42×C59 | SD16 | semidirect |
| 183. #1274 | D59 | semidirect |
| 209. C59 | #9301 | semidirect |
| 291. C42 | #11745660 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435023 | 2 |
| #21426844 | 2 |
| #21424928 | 2 |
| #21422776 | 2 |
| #21422657 | 2 |
| #21421955 | 2 |
| C59×#1274 | 2 |
| #9301 | 59 |