Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 125 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. Q8×D436 | C2 | semidirect |
| 3. #20295378 | C2 | semidirect |
| 4. #20295358 | C2 | semidirect |
| 5. #20295256 | C2 | semidirect |
| 6. #20295232 | C2 | semidirect |
| 7. #20295166 | C2 | semidirect |
| 8. C4×#13182016 | C2 | semidirect |
| 9. #20295091 | C2 | semidirect |
| 10. #103×D109 | C2 | semidirect |
| 11. #475×C109 | C2 | semidirect |
| 81. Q8×C109 | #41 | semidirect |
| 94. D436 | SD16 | semidirect |
| 129. C109 | #3298 | semidirect |
| 134. #475 | D109 | semidirect |
| 213. Q8 | #13182030 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D436 | 2 |
| #20295679 | 2 |
| #20295378 | 2 |
| #20295358 | 2 |
| #20295256 | 2 |
| #20295232 | 2 |
| #20295166 | 2 |
| C4×#13182016 | 2 |
| #20295091 | 2 |
| #103×D109 | 2 |
| #475×C109 | 2 |
| #3298 | 109 |