Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
420 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 139 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. D4×Dic218 | C2 | semidirect |
| 3. #20295377 | C2 | semidirect |
| 4. #20295357 | C2 | semidirect |
| 5. #20295312 | C2 | semidirect |
| 6. #20295255 | C2 | semidirect |
| 7. #20295232 | C2 | semidirect |
| 8. #20295167 | C2 | semidirect |
| 9. C4×#13182018 | C2 | semidirect |
| 10. C2×#16812624 | C2 | semidirect |
| 11. C8×D4×C109 | C2 | semidirect |
| 79. D4×C109 | SD16 | semidirect |
| 102. Dic218 | #41 | semidirect |
| 129. C109 | #3298 | semidirect |
| 139. C8×D4 | D109 | semidirect |
| 217. D4 | #13182018 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic218 | 2 |
| #20295680 | 2 |
| #20295377 | 2 |
| #20295357 | 2 |
| #20295312 | 2 |
| #20295255 | 2 |
| #20295232 | 2 |
| #20295167 | 2 |
| C4×#13182018 | 2 |
| C2×#16812624 | 2 |
| C8×D4×C109 | 2 |
| #3298 | 109 |