Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 392 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×Dic218 | C2 | semidirect |
| 3. #20295372 | C2 | semidirect |
| 4. #20295371 | C2 | semidirect |
| 5. #20295317 | C2 | semidirect |
| 6. #20295314 | C2 | semidirect |
| 7. #20295224 | C2 | semidirect |
| 8. #20295150 | C2 | semidirect |
| 9. SD16×Dic109 | C2 | semidirect |
| 10. C4×#13182016 | C2 | semidirect |
| 11. #460×C109 | C2 | semidirect |
| 77. Q8×C109 | #41 | semidirect |
| 99. Dic218 | SD16 | semidirect |
| 126. C109 | #3362 | semidirect |
| 134. #460 | D109 | semidirect |
| 206. Q8 | #13182028 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic218 | 2 |
| #20295696 | 2 |
| #20295372 | 2 |
| #20295371 | 2 |
| #20295317 | 2 |
| #20295314 | 2 |
| #20295224 | 2 |
| #20295150 | 2 |
| SD16×Dic109 | 2 |
| C4×#13182016 | 2 |
| #460×C109 | 2 |
| #3362 | 109 |