Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
518 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 518 conjugacy classes of subgroups — too many to draw. Only its 105 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. #21433136 | C2 | semidirect |
| 3. #21424103 | C2 | semidirect |
| 4. #21422655 | C2 | semidirect |
| 5. #21422496 | C2 | semidirect |
| 6. #21421991 | C2 | semidirect |
| 7. C59×#1286 | C2 | semidirect |
| 12. #16837608 | C4 | semidirect |
| 13. #16837598 | C4 | semidirect |
| 194. #1286 | D59 | semidirect |
| 221. C59 | #9309 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433562 | 2 |
| #21433136 | 2 |
| #21424103 | 2 |
| #21422655 | 2 |
| #21422496 | 2 |
| #21421991 | 2 |
| C59×#1286 | 2 |
| #9309 | 59 |