Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
478 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 75 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. C2×#15692281 | C2 | semidirect |
| 2. #20265744 | C2 | semidirect |
| 3. C2×#15692183 | C2 | semidirect |
| 4. #20265182 | C2 | semidirect |
| 5. C2×#15692172 | C2 | semidirect |
| 6. #20264937 | C2 | semidirect |
| 7. C2×#127×C101 | C2 | semidirect |
| 33. C2×Dic202 | D4 | semidirect |
| 34. C2×D404 | D4 | semidirect |
| 43. #13108058 | D4 | semidirect |
| 46. C4⋊Dic101 | D4 | semidirect |
| 65. C2×D4×C101 | D4 | semidirect |
| 69. C42×C101 | D4 | semidirect |
| 139. C101 | #2002 | semidirect |
| 142. C2×#127 | D101 | semidirect |
| 191. C2×D4 | C22⋊D101 | semidirect |
| 208. C42 | C22⋊D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692281 | 2 |
| #20265744 | 2 |
| C2×#15692183 | 2 |
| #20265182 | 2 |
| C2×#15692172 | 2 |
| #20264937 | 2 |
| C2×#127×C101 | 2 |
| #2002 | 101 |