Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
548 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 131 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. C2×#16812723 | C2 | semidirect |
| 2. #20295574 | C2 | semidirect |
| 3. C4×D4×D109 | C2 | semidirect |
| 4. #20295240 | C2 | semidirect |
| 5. #20295239 | C2 | semidirect |
| 6. #20295232 | C2 | semidirect |
| 7. #20295231 | C2 | semidirect |
| 8. #20295218 | C2 | semidirect |
| 9. #20295048 | C2 | semidirect |
| 10. #20295024 | C2 | semidirect |
| 11. #459×C109 | C2 | semidirect |
| 20. #16812699 | C22 | semidirect |
| 21. #16812686 | C22 | semidirect |
| 34. C4⋊#11724784 | C22 | semidirect |
| 35. #16812628 | C22 | semidirect |
| 36. #16812624 | C22 | semidirect |
| 37. #16812622 | C22 | semidirect |
| 38. #16812620 | C22 | semidirect |
| 40. #127×C109 | C22 | semidirect |
| 42. C4⋊C8×C109 | C22 | semidirect |
| 43. #102×C109 | C22 | semidirect |
| 52. D4×D109 | D4 | semidirect |
| 145. C4×C109 | AGL(1,ℤ/8) | semidirect |
| 161. C109 | #3036 | semidirect |
| 170. #459 | D109 | semidirect |
| 183. #127 | C2×D109 | semidirect |
| 200. C4⋊C8 | C2×D109 | semidirect |
| 204. #102 | C2×D109 | semidirect |
| 311. C4 | #16812723 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812723 | 2 |
| #20295574 | 2 |
| C4×D4×D109 | 2 |
| #20295240 | 2 |
| #20295239 | 2 |
| #20295232 | 2 |
| #20295231 | 2 |
| #20295218 | 2 |
| #20295048 | 2 |
| #20295024 | 2 |
| #459×C109 | 2 |
| #3036 | 109 |