Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
380 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 69 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. #20265975 | C2 | semidirect |
| 2. C2×#15692280 | C2 | semidirect |
| 3. #20265746 | C2 | semidirect |
| 4. #20265195 | C2 | semidirect |
| 5. #20265181 | C2 | semidirect |
| 6. #20264947 | C2 | semidirect |
| 7. #410×C101 | C2 | semidirect |
| 56. #13108058 | D4 | semidirect |
| 58. C2×#11717579 | D4 | semidirect |
| 64. C2×Q8×C101 | D4 | semidirect |
| 66. C2×D4×C101 | D4 | semidirect |
| 143. C101 | #2008 | semidirect |
| 149. #410 | D101 | semidirect |
| 184. C2×Q8 | D404 | semidirect |
| 195. C2×D4 | D404 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265975 | 2 |
| C2×#15692280 | 2 |
| #20265746 | 2 |
| #20265195 | 2 |
| #20265181 | 2 |
| #20264947 | 2 |
| #410×C101 | 2 |
| #2008 | 101 |