Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
524 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#16812705 | C2 | semidirect |
| 2. #20295593 | C2 | semidirect |
| 3. #20295276 | C2 | semidirect |
| 4. #20295259 | C2 | semidirect |
| 5. #20295064 | C2 | semidirect |
| 6. #20295031 | C2 | semidirect |
| 7. C22×D8×C109 | C2 | semidirect |
| 11. C2×#13182012 | C22 | semidirect |
| 12. C2×C8×D109 | C22 | semidirect |
| 15. #16812670 | C22 | semidirect |
| 18. #16812633 | C22 | semidirect |
| 19. #16812631 | C22 | semidirect |
| 20. #16812620 | C22 | semidirect |
| 49. C2×C8×C109 | D4 | semidirect |
| 94. C109 | #3058 | semidirect |
| 95. C22×D8 | D109 | semidirect |
| 139. C2×C8 | C22⋊D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812705 | 2 |
| #20295593 | 2 |
| #20295276 | 2 |
| #20295259 | 2 |
| #20295064 | 2 |
| #20295031 | 2 |
| C22×D8×C109 | 2 |
| #3058 | 109 |