Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
412 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 133 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. #20295581 | C2 | semidirect |
| 3. #20295424 | C2 | semidirect |
| 4. #20295376 | C2 | semidirect |
| 5. #20295372 | C2 | semidirect |
| 6. #20295252 | C2 | semidirect |
| 7. SD16×Dic109 | C2 | semidirect |
| 8. C4×C8×D109 | C2 | semidirect |
| 9. #492×C109 | C2 | semidirect |
| 86. C4×D109 | SD16 | semidirect |
| 89. C8×C109 | #41 | semidirect |
| 113. C109 | #3167 | semidirect |
| 117. #492 | D109 | semidirect |
| 203. C8 | #13182028 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295581 | 2 |
| #20295574 | 2 |
| #20295424 | 2 |
| #20295376 | 2 |
| #20295372 | 2 |
| #20295252 | 2 |
| SD16×Dic109 | 2 |
| C4×C8×D109 | 2 |
| #492×C109 | 2 |
| #3167 | 109 |