Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
604 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 604 conjugacy classes of subgroups — too many to draw. Only its 101 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×#16837838 | C2 | semidirect |
| 2. #21433705 | C2 | semidirect |
| 3. C2×#16837211 | C2 | semidirect |
| 4. #21425812 | C2 | semidirect |
| 5. C2×#16837184 | C2 | semidirect |
| 6. #21422203 | C2 | semidirect |
| 7. C2×C59×#469 | C2 | semidirect |
| 36. C2×Dic236 | D4 | semidirect |
| 38. C2×D472 | D4 | semidirect |
| 50. #14273667 | D4 | semidirect |
| 53. #14273661 | D4 | semidirect |
| 65. C2×D8×C59 | D4 | semidirect |
| 79. #106×C59 | D4 | semidirect |
| 216. C2×#469 | D59 | semidirect |
| 251. C59 | #13316 | semidirect |
| 268. C2×D8 | C22⋊D59 | semidirect |
| 298. #106 | C22⋊D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837838 | 2 |
| #21433705 | 2 |
| C2×#16837211 | 2 |
| #21425812 | 2 |
| C2×#16837184 | 2 |
| #21422203 | 2 |
| C2×C59×#469 | 2 |
| #13316 | 59 |