Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
706 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 706 conjugacy classes of subgroups — too many to draw. Only its 109 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. #21433136 | C2 | semidirect |
| 3. #21424085 | C2 | semidirect |
| 4. #21422764 | C2 | semidirect |
| 5. #21421998 | C2 | semidirect |
| 6. #21421997 | C2 | semidirect |
| 7. C59×#1545 | C2 | semidirect |
| 45. C4⋊(C59⋊C8) | D4 | semidirect |
| 62. C4⋊C8×C59 | D4 | semidirect |
| 194. #1545 | D59 | semidirect |
| 222. C59 | #9405 | semidirect |
| 254. C4⋊C8 | C22⋊D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433136 | 2 |
| #21429043 | 2 |
| #21424085 | 2 |
| #21422764 | 2 |
| #21421998 | 2 |
| #21421997 | 2 |
| C59×#1545 | 2 |
| #9405 | 59 |