Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
356 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 69 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. #21426324 | C2 | semidirect |
| 3. #21426234 | C2 | semidirect |
| 4. #21423485 | C2 | semidirect |
| 5. #21422146 | C2 | semidirect |
| 6. #21422058 | C2 | semidirect |
| 7. C59×D4⋊C16 | C2 | semidirect |
| 86. D472 | SD16 | semidirect |
| 141. D4⋊C16 | D59 | semidirect |
| 164. C59 | #12371 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435818 | 2 |
| #21426324 | 2 |
| #21426234 | 2 |
| #21423485 | 2 |
| #21422146 | 2 |
| #21422058 | 2 |
| C59×D4⋊C16 | 2 |
| #12371 | 59 |