Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
572 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 145 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×#15690831 | C2 | semidirect |
| 2. #20261286 | C2 | semidirect |
| 3. #20261283 | C2 | semidirect |
| 4. #20261116 | C2 | semidirect |
| 5. #20261114 | C2 | semidirect |
| 6. #20261111 | C2 | semidirect |
| 7. #20261108 | C2 | semidirect |
| 8. C4×C8×D97 | C2 | semidirect |
| 9. #492×C97 | C2 | semidirect |
| 47. C8×D97 | D4 | semidirect |
| 91. C4×C97 | #135 | semidirect |
| 102. C97 | #3147 | semidirect |
| 110. #492 | D97 | semidirect |
| 196. C4 | #15690831 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690831 | 2 |
| #20261286 | 2 |
| #20261283 | 2 |
| #20261116 | 2 |
| #20261114 | 2 |
| #20261111 | 2 |
| #20261108 | 2 |
| C4×C8×D97 | 2 |
| #492×C97 | 2 |
| #3147 | 97 |