Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
388 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 164 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. #20296076 | C2 | semidirect |
| 2. #20296060 | C2 | semidirect |
| 3. #20296055 | C2 | semidirect |
| 4. #20296048 | C2 | semidirect |
| 5. #20296042 | C2 | semidirect |
| 6. #20296030 | C2 | semidirect |
| 7. C2×C4⋊#11724786 | C2 | semidirect |
| 62. C2×C4×C109 | M16 | semidirect |
| 108. C109 | #2989 | semidirect |
| 185. C2×C4 | #13182039 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20296076 | 2 |
| #20296060 | 2 |
| #20296055 | 2 |
| #20296048 | 2 |
| #20296042 | 2 |
| #20296030 | 2 |
| C2×C4⋊#11724786 | 2 |
| #20295494 | 2 |
| #2989 | 109 |