Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
784 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 210 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. (C2×#87604)⋊Q8 | C2 | semidirect |
| 10. C22×Dic194 | C4 | semidirect |
| 11. C22×Dic194 | C4 | semidirect |
| 13. C2×Q8×D97 | C4 | semidirect |
| 17. C22×Q8×C97 | C4 | semidirect |
| 84. C97 | #2310 | semidirect |
| 94. C22×Q8 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690889 | 2 |
| (C2×#87604)⋊Q8 | 2 |
| #20261678 | 2 |
| C22×Q8×D97 | 2 |
| #2310 | 97 |