Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
414 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 3. #21425077 | C2 | semidirect |
| 4. #21422570 | C2 | semidirect |
| 5. #21421989 | C2 | semidirect |
| 6. #21421987 | C2 | semidirect |
| 9. #16837812 | C4 | semidirect |
| 10. #16837797 | C4 | semidirect |
| 11. #16837772 | C4 | semidirect |
| 12. #16837761 | C4 | semidirect |
| 233. C59 | #8998 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434703 | 2 |
| #21433266 | 2 |
| #21425077 | 2 |
| #21422570 | 2 |
| #21421989 | 2 |
| #21421987 | 2 |
| C59×#1500 | 2 |
| #8998 | 59 |