Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
368 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 368 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. #20295429 | C2 | semidirect |
| 3. #20295405 | C2 | semidirect |
| 4. #20295378 | C2 | semidirect |
| 5. #20295376 | C2 | semidirect |
| 7. C4×#13182019 | C2 | semidirect |
| 73. C2×C4×C109 | Q16 | semidirect |
| 105. C109 | #3170 | semidirect |
| 182. C2×C4 | #13182019 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295583 | 2 |
| #20295429 | 2 |
| #20295405 | 2 |
| #20295378 | 2 |
| #20295376 | 2 |
| #20295265 | 2 |
| C4×#13182019 | 2 |
| C2×C4×#11724784 | 2 |
| #533×C109 | 2 |
| #3170 | 109 |