Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
364 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 170 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. #20296077 | C2 | semidirect |
| 2. #20296076 | C2 | semidirect |
| 3. #20296075 | C2 | semidirect |
| 4. Q8×#11724786 | C2 | semidirect |
| 34. D109⋊C8 | Q8 | semidirect |
| 95. C109 | #2960 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20296077 | 2 |
| #20296076 | 2 |
| #20296075 | 2 |
| Q8×#11724786 | 2 |
| #20296033 | 2 |
| #20296030 | 2 |
| #20295991 | 2 |
| C4×D109⋊C8 | 2 |
| #20295581 | 2 |
| #2960 | 109 |