Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
188 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 61 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. #20265550 | C2 | semidirect |
| 2. #20265457 | C2 | semidirect |
| 4. #20264928 | C2 | semidirect |
| 5. #20264924 | C2 | semidirect |
| 6. #20264920 | C2 | semidirect |
| 7. C8×D4×C101 | C2 | semidirect |
| 46. D4×C101 | SD16 | semidirect |
| 63. C8×C101 | D8 | semidirect |
| 86. C101 | #1665 | semidirect |
| 90. C8×D4 | D101 | semidirect |
| 139. D4 | #13108063 | semidirect |
| 151. C8 | #13108059 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265550 | 2 |
| #20265457 | 2 |
| #20265372 | 2 |
| #20264928 | 2 |
| #20264924 | 2 |
| #20264920 | 2 |
| C8×D4×C101 | 2 |
| #1665 | 101 |