Finite Group DatabasebetaFinite Group DatabasebetaOrder 14272.
120 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 41 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×#16813157 | C2 | semidirect |
| 2. C2×#16813154 | C2 | semidirect |
| 4. #20297237 | C2 | semidirect |
| 5. #20297228 | C2 | semidirect |
| 6. #20297224 | C2 | semidirect |
| 7. C22⋊Q8×C223 | C2 | semidirect |
| 27. C223⋊C8 | D4 | semidirect |
| 55. C223 | #468 | semidirect |
| 59. C22⋊Q8 | D223 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813157 | 2 |
| C2×#16813154 | 2 |
| #20297278 | 2 |
| #20297237 | 2 |
| #20297228 | 2 |
| #20297224 | 2 |
| C22⋊Q8×C223 | 2 |
| #468 | 223 |