Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
646 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 646 conjugacy classes of subgroups — too many to draw. Only its 103 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. #21425767 | C2 | semidirect |
| 3. #21425745 | C2 | semidirect |
| 4. #21424071 | C2 | semidirect |
| 5. #21422224 | C2 | semidirect |
| 6. #21422216 | C2 | semidirect |
| 7. C59×#2884 | C2 | semidirect |
| 8. C2×#14273752 | C4 | semidirect |
| 9. C22×#11745671 | C4 | semidirect |
| 17. #16837411 | C4 | semidirect |
| 18. #16837398 | C4 | semidirect |
| 242. #2884 | D59 | semidirect |
| 278. C59 | #13103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433382 | 2 |
| #21425767 | 2 |
| #21425745 | 2 |
| #21424071 | 2 |
| #21422224 | 2 |
| #21422216 | 2 |
| C59×#2884 | 2 |
| #13103 | 59 |