Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
552 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 552 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×#15690842 | C2 | semidirect |
| 3. C4⋊Q8×D97 | C2 | semidirect |
| 4. #20261128 | C2 | semidirect |
| 5. #20261114 | C2 | semidirect |
| 6. #20261109 | C2 | semidirect |
| 7. #20261108 | C2 | semidirect |
| 8. C4×#13095494 | C2 | semidirect |
| 9. #494×C97 | C2 | semidirect |
| 46. #13095494 | D4 | semidirect |
| 89. C4×C97 | #137 | semidirect |
| 99. C97 | #3152 | semidirect |
| 105. #494 | D97 | semidirect |
| 191. C4 | #15690842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690842 | 2 |
| #20261286 | 2 |
| C4⋊Q8×D97 | 2 |
| #20261128 | 2 |
| #20261114 | 2 |
| #20261109 | 2 |
| #20261108 | 2 |
| C4×#13095494 | 2 |
| #494×C97 | 2 |
| #3152 | 97 |