Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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. #20295733 | C2 | semidirect |
| 2. #20295696 | C2 | semidirect |
| 3. #20295389 | C2 | semidirect |
| 4. #20295372 | C2 | semidirect |
| 5. #20295328 | C2 | semidirect |
| 6. #20295317 | C2 | semidirect |
| 7. #20295219 | C2 | semidirect |
| 8. #20295153 | C2 | semidirect |
| 9. #20295138 | C2 | semidirect |
| 10. C4×#13182014 | C2 | semidirect |
| 11. #459×C109 | C2 | semidirect |
| 82. D4×C109 | #41 | semidirect |
| 130. C109 | #3366 | semidirect |
| 138. #459 | D109 | semidirect |
| 218. D4 | #13182028 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295733 | 2 |
| #20295696 | 2 |
| #20295389 | 2 |
| #20295372 | 2 |
| #20295328 | 2 |
| #20295317 | 2 |
| #20295219 | 2 |
| #20295153 | 2 |
| #20295138 | 2 |
| C4×#13182014 | 2 |
| #459×C109 | 2 |
| #3366 | 109 |