Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
584 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 149 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×#16812725 | C2 | semidirect |
| 2. C4×#13182029 | C2 | semidirect |
| 3. #20295223 | C2 | semidirect |
| 4. #20295218 | C2 | semidirect |
| 5. #20295050 | C2 | semidirect |
| 6. #20295031 | C2 | semidirect |
| 7. C2×#127×C109 | C2 | semidirect |
| 10. C2×#13182017 | C22 | semidirect |
| 11. C2×#13182014 | C22 | semidirect |
| 13. C4×Dic218 | C22 | semidirect |
| 14. C4×D436 | C22 | semidirect |
| 19. C4⋊#11724784 | C22 | semidirect |
| 20. #16812620 | C22 | semidirect |
| 28. #13182029 | D4 | semidirect |
| 78. D436 | C2×D4 | semidirect |
| 82. Dic218 | C2×D4 | semidirect |
| 94. C4×C109 | AGL(1,ℤ/8) | semidirect |
| 105. C109 | #3038 | semidirect |
| 107. C2×#127 | D109 | semidirect |
| 201. C4 | #16812725 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812725 | 2 |
| C4×#13182029 | 2 |
| #20295223 | 2 |
| #20295218 | 2 |
| #20295050 | 2 |
| #20295031 | 2 |
| C2×#127×C109 | 2 |
| #3038 | 109 |