Finite Group DatabasebetaFinite Group DatabasebetaOrder 14272.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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. #20297299 | C2 | semidirect |
| 2. #20297295 | C2 | semidirect |
| 3. #20297293 | C2 | semidirect |
| 4. #20297289 | C2 | semidirect |
| 5. #20297280 | C2 | semidirect |
| 7. C4×D892 | C2 | semidirect |
| 8. C4×D892 | C2 | semidirect |
| 9. #20297261 | C2 | semidirect |
| 10. C42×D223 | C2 | semidirect |
| 11. C4×Q8×C223 | C2 | semidirect |
| 74. C223 | #529 | semidirect |
| 82. C4×Q8 | D223 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20297299 | 2 |
| #20297295 | 2 |
| #20297293 | 2 |
| #20297289 | 2 |
| #20297280 | 2 |
| #20297279 | 2 |
| C4×D892 | 2 |
| #20297261 | 2 |
| C42×D223 | 2 |
| C4×Q8×C223 | 2 |
| #529 | 223 |