Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
522 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 522 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 |
|---|---|---|
| 2. #21432898 | C2 | semidirect |
| 3. C2×#16837211 | C2 | semidirect |
| 4. #21425812 | C2 | semidirect |
| 5. #21422203 | C2 | semidirect |
| 6. #21422180 | C2 | semidirect |
| 7. C59×#1972 | C2 | semidirect |
| 11. #16837838 | C4 | semidirect |
| 47. #14273667 | C2×C4 | semidirect |
| 60. C2×D8×C59 | C2×C4 | semidirect |
| 115. Dic236 | C22⋊C4 | semidirect |
| 117. D472 | C22⋊C4 | semidirect |
| 183. #1972 | D59 | semidirect |
| 212. C59 | #13025 | semidirect |
| 227. C2×D8 | C4×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837838 | 2 |
| #21432898 | 2 |
| C2×#16837211 | 2 |
| #21425812 | 2 |
| #21422203 | 2 |
| #21422180 | 2 |
| C59×#1972 | 2 |
| #13025 | 59 |