Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
492 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 492 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. C22×#13182016 | C2 | semidirect |
| 2. C2×#16812707 | C2 | semidirect |
| 3. #20295600 | C2 | semidirect |
| 5. #20295275 | C2 | semidirect |
| 6. #20295258 | C2 | semidirect |
| 7. #20295062 | C2 | semidirect |
| 8. #20295032 | C2 | semidirect |
| 9. #419×C109 | C2 | semidirect |
| 16. C2×#13182012 | C22 | semidirect |
| 18. C2×C8×D109 | C22 | semidirect |
| 24. #16812675 | C22 | semidirect |
| 28. #16812632 | C22 | semidirect |
| 29. #16812630 | C22 | semidirect |
| 34. #103×C109 | C22 | semidirect |
| 50. C2×#11724784 | D4 | semidirect |
| 121. C109 | #3057 | semidirect |
| 129. #419 | D109 | semidirect |
| 154. #103 | C2×D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13182016 | 2 |
| C2×#16812707 | 2 |
| #20295600 | 2 |
| #20295595 | 2 |
| #20295275 | 2 |
| #20295258 | 2 |
| #20295062 | 2 |
| #20295032 | 2 |
| #419×C109 | 2 |
| #3057 | 109 |