Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
340 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 79 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. #20261501 | C2 | semidirect |
| 3. #20260717 | C2 | semidirect |
| 4. C2×#15690726 | C2 | semidirect |
| 5. C2×#15690726 | C2 | semidirect |
| 6. #20260505 | C2 | semidirect |
| 7. #344×C97 | C2 | semidirect |
| 45. #13095495 | D4 | semidirect |
| 55. M16×C97 | D4 | semidirect |
| 115. C97 | #1914 | semidirect |
| 122. #344 | D97 | semidirect |
| 166. M16 | D388 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261501 | 2 |
| #20261304 | 2 |
| #20260717 | 2 |
| C2×#15690726 | 2 |
| #20260505 | 2 |
| #344×C97 | 2 |
| #1914 | 97 |