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. #20295322 | C2 | semidirect |
| 4. #20295318 | C2 | semidirect |
| 5. #20295316 | C2 | semidirect |
| 6. #20295310 | C2 | semidirect |
| 7. #20295304 | C2 | semidirect |
| 8. #20295065 | C2 | semidirect |
| 9. #20295048 | C2 | semidirect |
| 11. #476×C109 | C2 | semidirect |
| 44. #13182028 | Q8 | semidirect |
| 86. D4×C109 | C2×Q8 | semidirect |
| 110. Dic218 | C2×Q8 | semidirect |
| 138. C109 | #3079 | semidirect |
| 144. #476 | D109 | semidirect |
| 229. D4 | 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×#13182028 | 2 |
| #20295322 | 2 |
| #20295318 | 2 |
| #20295316 | 2 |
| #20295310 | 2 |
| #20295304 | 2 |
| #20295065 | 2 |
| #20295048 | 2 |
| #20295024 | 2 |
| #476×C109 | 2 |
| #3079 | 109 |