Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
360 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 78 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. #20261739 | C2 | semidirect |
| 2. C2×#15690875 | C2 | semidirect |
| 3. C42×#87604 | C2 | semidirect |
| 11. #15690807 | C4 | semidirect |
| 12. #15690799 | C4 | semidirect |
| 16. C4⋊Q8×C97 | C4 | semidirect |
| 22. C4×#87604 | D4 | semidirect |
| 63. C4×C97 | #104 | semidirect |
| 73. C97 | #1962 | semidirect |
| 80. C4⋊Q8 | #87604 | semidirect |
| 139. C4 | #15690875 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261739 | 2 |
| C2×#15690875 | 2 |
| C42×#87604 | 2 |
| #20261286 | 2 |
| #1962 | 97 |