Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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. #20295563 | C2 | semidirect |
| 2. #20295427 | C2 | semidirect |
| 3. #20295411 | C2 | semidirect |
| 4. #20295382 | C2 | semidirect |
| 5. #20295264 | C2 | semidirect |
| 7. #20295258 | C2 | semidirect |
| 8. C4×#13182016 | C2 | semidirect |
| 9. C4×D872 | C2 | semidirect |
| 10. C4×C8×D109 | C2 | semidirect |
| 11. C4×Q16×C109 | C2 | semidirect |
| 119. C109 | #3168 | semidirect |
| 127. C4×Q16 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295563 | 2 |
| #20295427 | 2 |
| #20295411 | 2 |
| #20295382 | 2 |
| #20295264 | 2 |
| #20295263 | 2 |
| #20295258 | 2 |
| C4×#13182016 | 2 |
| C4×D872 | 2 |
| C4×C8×D109 | 2 |
| C4×Q16×C109 | 2 |
| #3168 | 109 |