Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
220 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 64 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 |
|---|---|---|
| 3. #20261648 | C2 | semidirect |
| 12. C2×Dic388 | C4 | semidirect |
| 16. Q16×D97 | C4 | semidirect |
| 19. C2×Q16×C97 | C4 | semidirect |
| 83. C97 | #2141 | semidirect |
| 95. C2×Q16 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261791 | 2 |
| #20261745 | 2 |
| #20261648 | 2 |
| C2×Q16×D97 | 2 |
| #2141 | 97 |