Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
572 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 572 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×#16812729 | C2 | semidirect |
| 2. C2×#16812724 | C2 | semidirect |
| 3. C2×#16812687 | C2 | semidirect |
| 4. #20295418 | C2 | semidirect |
| 5. #20295413 | C2 | semidirect |
| 6. #20295408 | C2 | semidirect |
| 7. C4×#13182013 | C2 | semidirect |
| 8. #532×C109 | C2 | semidirect |
| 13. C2×#13182019 | C22 | semidirect |
| 14. C2×#13182017 | C22 | semidirect |
| 22. #16812610 | C22 | semidirect |
| 23. C4×#11724784 | C22 | semidirect |
| 25. C4⋊Q8×C109 | C22 | semidirect |
| 26. #127×C109 | C22 | semidirect |
| 27. #124×C109 | C22 | semidirect |
| 43. #13182013 | D4 | semidirect |
| 107. C109 | #3153 | semidirect |
| 110. #532 | D109 | semidirect |
| 126. C4⋊Q8 | C2×D109 | semidirect |
| 127. #127 | C2×D109 | semidirect |
| 131. #124 | C2×D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812729 | 2 |
| C2×#16812724 | 2 |
| C2×#16812687 | 2 |
| #20295418 | 2 |
| #20295413 | 2 |
| #20295408 | 2 |
| C4×#13182013 | 2 |
| #532×C109 | 2 |
| #3153 | 109 |