Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 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 |
|---|---|---|
| 2. C22×#13182016 | C2 | semidirect |
| 3. #20295500 | C2 | semidirect |
| 4. #20295238 | C2 | semidirect |
| 5. #20295228 | C2 | semidirect |
| 6. #20295053 | C2 | semidirect |
| 7. #20295035 | C2 | semidirect |
| 8. #20295022 | C2 | semidirect |
| 9. #536×C109 | C2 | semidirect |
| 22. C4⋊#11724784 | C22 | semidirect |
| 23. #16812623 | C22 | semidirect |
| 24. #16812623 | C22 | semidirect |
| 25. #16812620 | C22 | semidirect |
| 28. C4⋊Q8×C109 | C22 | semidirect |
| 29. #124×C109 | C22 | semidirect |
| 117. C109 | #3042 | semidirect |
| 120. #536 | D109 | semidirect |
| 137. C4⋊Q8 | C2×D109 | semidirect |
| 138. #124 | C2×D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812724 | 2 |
| C22×#13182016 | 2 |
| #20295500 | 2 |
| #20295238 | 2 |
| #20295228 | 2 |
| #20295053 | 2 |
| #20295035 | 2 |
| #20295022 | 2 |
| #536×C109 | 2 |
| #3042 | 109 |