Finite Group DatabasebetaFinite Group DatabasebetaOrder 15424.
114 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 114 conjugacy classes of subgroups — too many to draw. Only its 39 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. C4⋊C4×D241 | C2 | semidirect |
| 3. #21440574 | C2 | semidirect |
| 4. #21440573 | C2 | semidirect |
| 5. #21440563 | C2 | semidirect |
| 6. #21440554 | C2 | semidirect |
| 7. #102×C241 | C2 | semidirect |
| 52. C241 | #481 | semidirect |
| 59. #102 | D241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21440613 | 2 |
| C4⋊C4×D241 | 2 |
| #21440574 | 2 |
| #21440573 | 2 |
| #21440563 | 2 |
| #21440554 | 2 |
| #102×C241 | 2 |
| #481 | 241 |