Finite Group DatabasebetaFinite Group DatabasebetaOrder 14272.
270 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 103 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×Q8×D223 | C2 | semidirect |
| 3. #20297303 | C2 | semidirect |
| 4. #20297290 | C2 | semidirect |
| 5. #20297289 | C2 | semidirect |
| 6. #20297286 | C2 | semidirect |
| 7. #20297284 | C2 | semidirect |
| 8. #20297283 | C2 | semidirect |
| 9. #20297280 | C2 | semidirect |
| 10. #20297262 | C2 | semidirect |
| 11. C22⋊Q8×C223 | C2 | semidirect |
| 83. C223 | #536 | semidirect |
| 94. C22⋊Q8 | D223 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813170 | 2 |
| C2×Q8×D223 | 2 |
| #20297303 | 2 |
| #20297290 | 2 |
| #20297289 | 2 |
| #20297286 | 2 |
| #20297284 | 2 |
| #20297283 | 2 |
| #20297280 | 2 |
| #20297262 | 2 |
| C22⋊Q8×C223 | 2 |
| #536 | 223 |