Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
346 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 2. #20265651 | C2 | semidirect |
| 3. #20265193 | C2 | semidirect |
| 4. #20265183 | C2 | semidirect |
| 5. #20265150 | C2 | semidirect |
| 6. #20264934 | C2 | semidirect |
| 7. #344×C101 | C2 | semidirect |
| 12. C2×#13108063 | C4 | semidirect |
| 13. C2×D808 | C4 | semidirect |
| 30. C2×Dic202 | C2×C4 | semidirect |
| 35. C2×D404 | C2×C4 | semidirect |
| 56. C2×C8×C101 | C2×C4 | semidirect |
| 116. C101 | #1904 | semidirect |
| 122. #344 | D101 | semidirect |
| 165. C2×C8 | C4×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692283 | 2 |
| #20265651 | 2 |
| #20265193 | 2 |
| #20265183 | 2 |
| #20265150 | 2 |
| #20264934 | 2 |
| #344×C101 | 2 |
| #1904 | 101 |