Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
412 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 412 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. #20295422 | C2 | semidirect |
| 3. #20295400 | C2 | semidirect |
| 4. #20295376 | C2 | semidirect |
| 5. #20295374 | C2 | semidirect |
| 6. #20295257 | C2 | semidirect |
| 7. C4×#13182016 | C2 | semidirect |
| 8. C2×C4×#11724784 | C2 | semidirect |
| 9. #533×C109 | C2 | semidirect |
| 75. C2×C4×C109 | SD16 | semidirect |
| 90. #11724784 | #41 | semidirect |
| 113. C109 | #3167 | semidirect |
| 114. #533 | D109 | semidirect |
| 195. C2×C4 | #13182016 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295576 | 2 |
| #20295422 | 2 |
| #20295400 | 2 |
| #20295376 | 2 |
| #20295374 | 2 |
| #20295257 | 2 |
| C4×#13182016 | 2 |
| C2×C4×#11724784 | 2 |
| #533×C109 | 2 |
| #3167 | 109 |