Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 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. #20295504 | C2 | semidirect |
| 4. #20295129 | C2 | semidirect |
| 5. #20295111 | C2 | semidirect |
| 6. #20295062 | C2 | semidirect |
| 8. #20294984 | C2 | semidirect |
| 9. #419×C109 | C2 | semidirect |
| 11. C2×#13182016 | C4 | semidirect |
| 16. Q8×Dic109 | C22 | semidirect |
| 23. #16812632 | C22 | semidirect |
| 24. #16812630 | C22 | semidirect |
| 26. #16812609 | C22 | semidirect |
| 27. C8×Dic109 | C22 | semidirect |
| 31. #103×C109 | C22 | semidirect |
| 38. #13182016 | C2×C4 | semidirect |
| 39. #13182016 | C2×C4 | semidirect |
| 40. C2×#11724784 | C2×C4 | semidirect |
| 54. C2×Q8×C109 | C2×C4 | semidirect |
| 104. C109 | #2949 | semidirect |
| 111. #419 | D109 | semidirect |
| 132. #103 | C2×D109 | semidirect |
| 139. C2×Q8 | C4×D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13182016 | 2 |
| #20295504 | 2 |
| #20295500 | 2 |
| #20295129 | 2 |
| #20295111 | 2 |
| #20295062 | 2 |
| #20295032 | 2 |
| #20294984 | 2 |
| #419×C109 | 2 |
| #2949 | 109 |