Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
444 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 83 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. #20261209 | C2 | semidirect |
| 3. #20260741 | C2 | semidirect |
| 4. #20260739 | C2 | semidirect |
| 5. C2×#15690726 | C2 | semidirect |
| 6. #20260495 | C2 | semidirect |
| 7. #339×C97 | C2 | semidirect |
| 13. #15690807 | C4 | semidirect |
| 38. C2×D388 | C2×C4 | semidirect |
| 44. C4⋊Dic97 | D4 | semidirect |
| 53. C4⋊C4×C97 | D4 | semidirect |
| 57. C42×C97 | C2×C4 | semidirect |
| 115. C97 | #1887 | semidirect |
| 122. #339 | D97 | semidirect |
| 165. C4⋊C4 | D388 | semidirect |
| 172. C42 | C4×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690807 | 2 |
| #20261209 | 2 |
| #20260741 | 2 |
| #20260739 | 2 |
| C2×#15690726 | 2 |
| #20260495 | 2 |
| #339×C97 | 2 |
| #1887 | 97 |