Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
532 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×Q16×D97 | C2 | semidirect |
| 4. #20261310 | C2 | semidirect |
| 5. #20261128 | C2 | semidirect |
| 6. #20261127 | C2 | semidirect |
| 7. #20261120 | C2 | semidirect |
| 8. #20261119 | C2 | semidirect |
| 9. #20261113 | C2 | semidirect |
| 10. #20260689 | C2 | semidirect |
| 11. #494×C97 | C2 | semidirect |
| 122. C97 | #3156 | semidirect |
| 132. #494 | 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×#15690833 | 2 |
| C2×Q16×D97 | 2 |
| #20261310 | 2 |
| #20261128 | 2 |
| #20261127 | 2 |
| #20261120 | 2 |
| #20261119 | 2 |
| #20261113 | 2 |
| #20260689 | 2 |
| #494×C97 | 2 |
| #3156 | 97 |