Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
398 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 166 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. #20296057 | C2 | semidirect |
| 3. D4×#11724786 | C2 | semidirect |
| 4. #20296046 | C2 | semidirect |
| 5. #20296043 | C2 | semidirect |
| 6. #20296029 | C2 | semidirect |
| 7. C2×#16812766 | C2 | semidirect |
| 64. D4×C109 | M16 | semidirect |
| 108. C109 | #2990 | semidirect |
| 172. D4 | #13182038 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20296077 | 2 |
| #20296057 | 2 |
| D4×#11724786 | 2 |
| #20296046 | 2 |
| #20296043 | 2 |
| #20296029 | 2 |
| C2×#16812766 | 2 |
| #41×Dic109 | 2 |
| #2990 | 109 |