Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
484 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 221 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. #20261218 | C2 | semidirect |
| 2. #20260836 | C2 | semidirect |
| 3. Q16×Dic97 | C2 | semidirect |
| 4. D8×Dic97 | C2 | semidirect |
| 5. C2×#15690744 | C2 | semidirect |
| 6. #20260736 | C2 | semidirect |
| 7. #20260690 | C2 | semidirect |
| 24. #135×C97 | C4 | semidirect |
| 43. #41×C97 | C2×C4 | semidirect |
| 49. Q16×C97 | C2×C4 | semidirect |
| 50. SD16×C97 | C2×C4 | semidirect |
| 51. D8×C97 | C2×C4 | semidirect |
| 52. C2×C8×C97 | C2×C4 | semidirect |
| 96. C97 | #2951 | semidirect |
| 106. #135 | Dic97 | semidirect |
| 126. #41 | C2×Dic97 | semidirect |
| 134. Q16 | C2×Dic97 | semidirect |
| 135. SD16 | C2×Dic97 | semidirect |
| 136. D8 | C2×Dic97 | semidirect |
| 139. C2×C8 | C2×Dic97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261218 | 2 |
| #20260836 | 2 |
| Q16×Dic97 | 2 |
| D8×Dic97 | 2 |
| C2×#15690744 | 2 |
| #20260736 | 2 |
| #20260690 | 2 |
| C2×#135×C97 | 2 |
| #2951 | 97 |