Finite Group DatabasebetaFinite Group DatabasebetaOrder 14912.
134 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 56 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. C2×#16836602 | C2 | semidirect |
| 2. C22×#14272345 | C2 | semidirect |
| 3. #21418602 | C2 | semidirect |
| 4. #21418592 | C2 | semidirect |
| 5. C22⋊#14272345 | C2 | semidirect |
| 6. C4×#14272345 | C2 | semidirect |
| 24. #14272345 | D4 | semidirect |
| 26. C22⋊D233 | C8 | semidirect |
| 39. C22×C233 | C2×C8 | semidirect |
| 43. C2×D233 | C2×C8 | semidirect |
| 47. Dic233 | C2×C8 | semidirect |
| 55. C233 | C8×D4 | semidirect |
| 98. C22 | #16836602 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16836602 | 2 |
| C22×#14272345 | 2 |
| #21418602 | 2 |
| #21418592 | 2 |
| C22⋊#14272345 | 2 |
| C4×#14272345 | 2 |
| #21418495 | 2 |
| C8×D4 | 233 |