Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
440 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 145 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 |
|---|---|---|
| 2. #20295323 | C2 | semidirect |
| 3. #20295313 | C2 | semidirect |
| 4. #20295303 | C2 | semidirect |
| 5. #20295069 | C2 | semidirect |
| 6. #20295050 | C2 | semidirect |
| 8. #533×C109 | C2 | semidirect |
| 18. #16812632 | C22 | semidirect |
| 19. #16812630 | C22 | semidirect |
| 20. C4⋊#11724784 | C22 | semidirect |
| 21. C4⋊#11724784 | C22 | semidirect |
| 24. C4⋊Q8×C109 | C22 | semidirect |
| 25. C4⋊Q8×C109 | C22 | semidirect |
| 26. #125×C109 | C22 | semidirect |
| 36. C2×D436 | Q8 | semidirect |
| 116. C109 | #3077 | semidirect |
| 117. #533 | D109 | semidirect |
| 128. C4⋊Q8 | C2×D109 | semidirect |
| 129. C4⋊Q8 | C2×D109 | semidirect |
| 130. #125 | C2×D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D436 | 2 |
| #20295323 | 2 |
| #20295313 | 2 |
| #20295303 | 2 |
| #20295069 | 2 |
| #20295050 | 2 |
| #20295030 | 2 |
| #533×C109 | 2 |
| #3077 | 109 |