Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
250 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 59 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. D4×Dic202 | C2 | semidirect |
| 2. #20265524 | C2 | semidirect |
| 3. #20265378 | C2 | semidirect |
| 5. #20264924 | C2 | semidirect |
| 6. #20264909 | C2 | semidirect |
| 7. D4⋊C8×C101 | C2 | semidirect |
| 54. D4×C101 | SD16 | semidirect |
| 74. Dic202 | D8 | semidirect |
| 100. C101 | #1627 | semidirect |
| 107. D4⋊C8 | D101 | semidirect |
| 164. D4 | #13108063 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic202 | 2 |
| #20265524 | 2 |
| #20265378 | 2 |
| #20265372 | 2 |
| #20264924 | 2 |
| #20264909 | 2 |
| D4⋊C8×C101 | 2 |
| #1627 | 101 |