Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
780 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 97 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×#16837789 | C2 | semidirect |
| 2. #21432141 | C2 | semidirect |
| 3. #21424921 | C2 | semidirect |
| 4. C2×#16837142 | C2 | semidirect |
| 5. C2×#16837141 | C2 | semidirect |
| 6. #21421978 | C2 | semidirect |
| 7. C2×C59×#496 | C2 | semidirect |
| 53. #14273638 | D4 | semidirect |
| 70. #127×C59 | D4 | semidirect |
| 79. #97×C59 | D4 | semidirect |
| 226. C2×#496 | D59 | semidirect |
| 263. C59 | #10078 | semidirect |
| 286. #127 | C22⋊D59 | 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×#16837789 | 2 |
| #21432141 | 2 |
| #21424921 | 2 |
| C2×#16837142 | 2 |
| C2×#16837141 | 2 |
| #21421978 | 2 |
| C2×C59×#496 | 2 |
| #10078 | 59 |