Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
496 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 89 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. #21432732 | C2 | semidirect |
| 3. #21422695 | C2 | semidirect |
| 4. #21422693 | C2 | semidirect |
| 5. #21422428 | C2 | semidirect |
| 6. #21421989 | C2 | semidirect |
| 7. C59×#1300 | C2 | semidirect |
| 61. #14273638 | D4 | semidirect |
| 71. #97×C59 | D4 | semidirect |
| 218. #1300 | D59 | semidirect |
| 249. C59 | #9389 | semidirect |
| 287. #97 | D236 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432732 | 2 |
| #21429777 | 2 |
| #21422695 | 2 |
| #21422693 | 2 |
| #21422428 | 2 |
| #21421989 | 2 |
| C59×#1300 | 2 |
| #9389 | 59 |