Finite Group DatabasebetaFinite Group DatabasebetaOrder 14272.
258 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 107 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. #20297350 | C2 | semidirect |
| 2. #20297335 | C2 | semidirect |
| 3. #20297329 | C2 | semidirect |
| 4. #20297324 | C2 | semidirect |
| 5. C2×#16813157 | C2 | semidirect |
| 6. #20297311 | C2 | semidirect |
| 7. 2−1+4×C223 | C2 | semidirect |
| 12. #16813160 | C22 | semidirect |
| 13. #16813158 | C22 | semidirect |
| 14. #16813157 | C22 | semidirect |
| 15. #16813157 | C22 | semidirect |
| 16. #16813155 | C22 | semidirect |
| 17. #16813154 | C22 | semidirect |
| 18. C2×C223⋊C8 | C22 | semidirect |
| 21. #41×C223 | C22 | semidirect |
| 23. C2×Q8×C223 | C22 | semidirect |
| 53. C223 | #577 | semidirect |
| 55. 2−1+4 | D223 | semidirect |
| 66. #41 | C2×D223 | semidirect |
| 68. C2×Q8 | C2×D223 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20297350 | 2 |
| #20297335 | 2 |
| #20297329 | 2 |
| #20297324 | 2 |
| C2×#16813157 | 2 |
| #20297311 | 2 |
| 2−1+4×C223 | 2 |
| #577 | 223 |