Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 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. #20265645 | C2 | semidirect |
| 3. #20265288 | C2 | semidirect |
| 4. #20265283 | C2 | semidirect |
| 5. #20265276 | C2 | semidirect |
| 6. #20265171 | C2 | semidirect |
| 7. C2×#15692165 | C2 | semidirect |
| 8. #427×C101 | C2 | semidirect |
| 10. #15692277 | C4 | semidirect |
| 30. #13108074 | C2×C4 | semidirect |
| 37. Dic404 | C2×C4 | semidirect |
| 38. #13108063 | C2×C4 | semidirect |
| 39. D808 | C2×C4 | semidirect |
| 48. C2×C8×C101 | C2×C4 | semidirect |
| 90. C101 | #2943 | semidirect |
| 96. #427 | D101 | semidirect |
| 133. 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×#15692277 | 2 |
| #20265645 | 2 |
| #20265288 | 2 |
| #20265283 | 2 |
| #20265276 | 2 |
| #20265171 | 2 |
| C2×#15692165 | 2 |
| #427×C101 | 2 |
| #2943 | 101 |