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. #20265977 | C2 | semidirect |
| 2. C2×#15692281 | C2 | semidirect |
| 3. #20265744 | C2 | semidirect |
| 4. #20265195 | C2 | semidirect |
| 5. #20265150 | C2 | semidirect |
| 6. #20264948 | C2 | semidirect |
| 7. #418×C101 | C2 | semidirect |
| 40. C2×Dic202 | D4 | semidirect |
| 42. C2×D404 | D4 | semidirect |
| 55. #13108058 | D4 | semidirect |
| 71. C2×C8×C101 | D4 | semidirect |
| 143. C101 | #2008 | semidirect |
| 148. #418 | D101 | semidirect |
| 210. C2×C8 | C22⋊D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265977 | 2 |
| C2×#15692281 | 2 |
| #20265744 | 2 |
| #20265195 | 2 |
| #20265150 | 2 |
| #20264948 | 2 |
| #418×C101 | 2 |
| #2008 | 101 |