Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
648 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 173 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 |
|---|---|---|
| 2. #20260615 | C2 | semidirect |
| 3. #20260614 | C2 | semidirect |
| 4. #20260613 | C2 | semidirect |
| 5. #20260612 | C2 | semidirect |
| 6. #20260611 | C2 | semidirect |
| 7. #20260611 | C2 | semidirect |
| 8. #20260602 | C2 | semidirect |
| 9. #386×C97 | C2 | semidirect |
| 15. #15690806 | C4 | semidirect |
| 35. C2×D388 | C2×C4 | semidirect |
| 40. C2×C22⋊D97 | C2×C4 | semidirect |
| 41. C2×C22⋊D97 | C2×C4 | semidirect |
| 55. C4×Dic97 | C2×C4 | semidirect |
| 60. C2×D4×C97 | C2×C4 | semidirect |
| 148. C97 | #2380 | semidirect |
| 156. #386 | D97 | semidirect |
| 194. C2×D4 | C4×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690806 | 2 |
| #20260615 | 2 |
| #20260614 | 2 |
| #20260613 | 2 |
| #20260612 | 2 |
| #20260611 | 2 |
| #20260602 | 2 |
| #386×C97 | 2 |
| #2380 | 97 |