Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
192 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 64 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. #20266205 | C2 | semidirect |
| 2. D4×#11717581 | C2 | semidirect |
| 3. #20266039 | C2 | semidirect |
| 4. #20266025 | C2 | semidirect |
| 5. D4⋊#11717581 | C2 | semidirect |
| 6. #20266018 | C2 | semidirect |
| 33. #13108059 | C8 | semidirect |
| 45. D4×C101 | C2×C8 | semidirect |
| 54. D404 | C2×C8 | semidirect |
| 63. #11717579 | C2×C8 | semidirect |
| 84. C101 | #1580 | semidirect |
| 131. D4 | D101⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20266205 | 2 |
| D4×#11717581 | 2 |
| #20266039 | 2 |
| #20266025 | 2 |
| D4⋊#11717581 | 2 |
| #20266018 | 2 |
| #20265257 | 2 |
| #1580 | 101 |