Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
552 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 141 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×#15690842 | C2 | semidirect |
| 2. C2×#15690839 | C2 | semidirect |
| 4. C4⋊Q8×D97 | C2 | semidirect |
| 5. #20261130 | C2 | semidirect |
| 6. #20261129 | C2 | semidirect |
| 7. #20261127 | C2 | semidirect |
| 8. #20261113 | C2 | semidirect |
| 9. #20261106 | C2 | semidirect |
| 10. #20260687 | C2 | semidirect |
| 11. #497×C97 | C2 | semidirect |
| 63. #13095494 | D4 | semidirect |
| 124. Dic97 | #137 | semidirect |
| 131. C97 | #3152 | semidirect |
| 139. #497 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690842 | 2 |
| C2×#15690839 | 2 |
| #20261284 | 2 |
| C4⋊Q8×D97 | 2 |
| #20261130 | 2 |
| #20261129 | 2 |
| #20261127 | 2 |
| #20261113 | 2 |
| #20261106 | 2 |
| #20260687 | 2 |
| #497×C97 | 2 |
| #3152 | 97 |