Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
426 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 426 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 |
|---|---|---|
| 1. #20295698 | C2 | semidirect |
| 2. #20295374 | C2 | semidirect |
| 3. #20295303 | C2 | semidirect |
| 4. #20295221 | C2 | semidirect |
| 5. Q8×#11724784 | C2 | semidirect |
| 6. C4×#13182014 | C2 | semidirect |
| 7. D4×Q8×C109 | C2 | semidirect |
| 47. Q8×C109 | D8 | semidirect |
| 49. D4×C109 | #41 | semidirect |
| 82. C109 | #3358 | semidirect |
| 84. D4×Q8 | D109 | semidirect |
| 129. Q8 | #13182014 | semidirect |
| 135. D4 | #13182030 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295698 | 2 |
| #20295374 | 2 |
| #20295303 | 2 |
| #20295221 | 2 |
| Q8×#11724784 | 2 |
| C4×#13182014 | 2 |
| D4×Q8×C109 | 2 |
| #3358 | 109 |