Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1318 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 1318 conjugacy classes of subgroups — too many to draw. Only its 191 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 |
|---|---|---|
| 1. C2×#16838014 | C2 | semidirect |
| 4. #21425243 | C2 | semidirect |
| 5. #21425181 | C2 | semidirect |
| 6. #21424450 | C2 | semidirect |
| 7. #21424406 | C2 | semidirect |
| 8. C59×#1818 | C2 | semidirect |
| 12. C2×#14273727 | C22 | semidirect |
| 14. C2×#14273719 | C22 | semidirect |
| 17. C2×C4×Dic118 | C22 | semidirect |
| 20. C2×#14273652 | C22 | semidirect |
| 26. #16837165 | C22 | semidirect |
| 29. C59×#336 | C22 | semidirect |
| 30. C59×#336 | C22 | semidirect |
| 188. #1818 | D59 | semidirect |
| 215. #336 | C2×D59 | semidirect |
| 216. #336 | C2×D59 | semidirect |
| 217. C59 | #23942 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16838014 | 2 |
| C2×#16837555 | 2 |
| #21426676 | 2 |
| #21425243 | 2 |
| #21425181 | 2 |
| #21424450 | 2 |
| #21424406 | 2 |
| C59×#1818 | 2 |
| #23942 | 59 |