Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 141 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. #20295654 | C2 | semidirect |
| 3. #20295327 | C2 | semidirect |
| 4. #20295327 | C2 | semidirect |
| 5. #20295317 | C2 | semidirect |
| 6. #20295307 | C2 | semidirect |
| 7. #20295068 | C2 | semidirect |
| 8. #20295064 | C2 | semidirect |
| 11. #424×C109 | C2 | semidirect |
| 13. #16812699 | C22 | semidirect |
| 15. #16812691 | C22 | semidirect |
| 26. #16812633 | C22 | semidirect |
| 27. #16812633 | C22 | semidirect |
| 28. #16812633 | C22 | semidirect |
| 29. #16812631 | C22 | semidirect |
| 30. #16812631 | C22 | semidirect |
| 31. #16812631 | C22 | semidirect |
| 39. C4⋊C8×C109 | C22 | semidirect |
| 40. C4⋊C8×C109 | C22 | semidirect |
| 45. C2×D436 | Q8 | semidirect |
| 125. C109 | #3081 | semidirect |
| 134. #424 | D109 | semidirect |
| 160. C4⋊C8 | C2×D109 | semidirect |
| 161. C4⋊C8 | C2×D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295654 | 2 |
| #20295500 | 2 |
| #20295327 | 2 |
| #20295317 | 2 |
| #20295307 | 2 |
| #20295068 | 2 |
| #20295064 | 2 |
| #20295032 | 2 |
| C2×#16812621 | 2 |
| #424×C109 | 2 |
| #3081 | 109 |