Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
780 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 95 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×#16837792 | C2 | semidirect |
| 2. C2×#16837791 | C2 | semidirect |
| 3. #21432141 | C2 | semidirect |
| 4. #21424920 | C2 | semidirect |
| 5. C2×#16837141 | C2 | semidirect |
| 6. #21421978 | C2 | semidirect |
| 7. C2×C59×#329 | C2 | semidirect |
| 49. #14273724 | D4 | semidirect |
| 61. #14273638 | D4 | semidirect |
| 79. #97×C59 | D4 | semidirect |
| 230. C2×#329 | D59 | semidirect |
| 263. C59 | #10078 | semidirect |
| 309. #97 | C22⋊D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837792 | 2 |
| C2×#16837791 | 2 |
| #21432141 | 2 |
| #21424920 | 2 |
| C2×#16837141 | 2 |
| #21421978 | 2 |
| C2×C59×#329 | 2 |
| #10078 | 59 |