Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
256 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 16. #15690720 | C4 | semidirect |
| 63. C8×C97 | C4⋊C4 | semidirect |
| 64. #11715895 | C4⋊C4 | semidirect |
| 85. C97 | #1847 | semidirect |
| 149. C8 | #13095490 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690743 | 2 |
| C2×#15690742 | 2 |
| C2×#15690741 | 2 |
| C2×#15690720 | 2 |
| #20260604 | 2 |
| #20260600 | 2 |
| C2×#107×C97 | 2 |
| #1847 | 97 |