Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
430 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 119 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. #20295574 | C2 | semidirect |
| 2. C4×#13182030 | C2 | semidirect |
| 3. #20295348 | C2 | semidirect |
| 4. #20295311 | C2 | semidirect |
| 5. #20295307 | C2 | semidirect |
| 6. #20295218 | C2 | semidirect |
| 7. #20295170 | C2 | semidirect |
| 8. #20295135 | C2 | semidirect |
| 9. #20295127 | C2 | semidirect |
| 10. #20295082 | C2 | semidirect |
| 11. #460×C109 | C2 | semidirect |
| 87. Q8×C109 | #41 | semidirect |
| 106. D436 | #41 | semidirect |
| 145. C109 | #3115 | semidirect |
| 151. #460 | D109 | semidirect |
| 233. Q8 | #13182028 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295574 | 2 |
| C4×#13182030 | 2 |
| #20295348 | 2 |
| #20295311 | 2 |
| #20295307 | 2 |
| #20295218 | 2 |
| #20295170 | 2 |
| #20295135 | 2 |
| #20295127 | 2 |
| #20295082 | 2 |
| #460×C109 | 2 |
| #3115 | 109 |