Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
406 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 406 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. #21425868 | C2 | semidirect |
| 5. #21424845 | C2 | semidirect |
| 6. #21422177 | C2 | semidirect |
| 7. C59×#1384 | C2 | semidirect |
| 21. #16837211 | C4 | semidirect |
| 43. #14273667 | C2×C4 | semidirect |
| 60. #106×C59 | C2×C4 | semidirect |
| 155. #1384 | D59 | semidirect |
| 180. C59 | #12951 | semidirect |
| 210. #106 | C4×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432867 | 2 |
| #21425868 | 2 |
| #21425846 | 2 |
| #21425831 | 2 |
| #21424845 | 2 |
| #21422177 | 2 |
| C59×#1384 | 2 |
| #12951 | 59 |