Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
416 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 133 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. C4⋊Q8×D109 | C2 | semidirect |
| 3. #20295319 | C2 | semidirect |
| 4. #20295315 | C2 | semidirect |
| 5. #20295311 | C2 | semidirect |
| 6. #20295307 | C2 | semidirect |
| 7. #20295303 | C2 | semidirect |
| 8. #20295065 | C2 | semidirect |
| 9. #20295048 | C2 | semidirect |
| 11. #475×C109 | C2 | semidirect |
| 44. #13182030 | Q8 | semidirect |
| 86. Q8×C109 | C2×Q8 | semidirect |
| 100. D436 | C2×Q8 | semidirect |
| 138. C109 | #3079 | semidirect |
| 144. #475 | D109 | semidirect |
| 226. Q8 | Q8×D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D109 | 2 |
| C4×#13182030 | 2 |
| #20295319 | 2 |
| #20295315 | 2 |
| #20295311 | 2 |
| #20295307 | 2 |
| #20295303 | 2 |
| #20295065 | 2 |
| #20295048 | 2 |
| #20295026 | 2 |
| #475×C109 | 2 |
| #3079 | 109 |