Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
478 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 99 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. #21425072 | C2 | semidirect |
| 5. #21422518 | C2 | semidirect |
| 6. #21421928 | C2 | semidirect |
| 7. C59×#1299 | C2 | semidirect |
| 11. #16837688 | C4 | semidirect |
| 12. #16837683 | C4 | semidirect |
| 13. #16837613 | C4 | semidirect |
| 14. #16837608 | C4 | semidirect |
| 206. #1299 | D59 | semidirect |
| 238. C59 | #8971 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434168 | 2 |
| #21433222 | 2 |
| #21425072 | 2 |
| C4×#14273653 | 2 |
| #21422518 | 2 |
| #21421928 | 2 |
| C59×#1299 | 2 |
| #8971 | 59 |