Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
492 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 175 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. C4×#13108073 | C2 | semidirect |
| 3. #20265289 | C2 | semidirect |
| 4. #20265285 | C2 | semidirect |
| 5. #20265283 | C2 | semidirect |
| 6. #20265277 | C2 | semidirect |
| 7. #20265274 | C2 | semidirect |
| 8. #20265212 | C2 | semidirect |
| 9. #20265170 | C2 | semidirect |
| 10. #97×D101 | C2 | semidirect |
| 11. #442×C101 | C2 | semidirect |
| 13. #15692274 | C4 | semidirect |
| 41. #13108073 | C2×C4 | semidirect |
| 48. Dic404 | C2×C4 | semidirect |
| 49. #13108062 | C2×C4 | semidirect |
| 53. C8×D101 | C2×C4 | semidirect |
| 66. D8×C101 | C2×C4 | semidirect |
| 115. C101 | #2943 | semidirect |
| 119. #442 | D101 | semidirect |
| 167. D8 | C4×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692274 | 2 |
| C4×#13108073 | 2 |
| #20265289 | 2 |
| #20265285 | 2 |
| #20265283 | 2 |
| #20265277 | 2 |
| #20265274 | 2 |
| #20265212 | 2 |
| #20265170 | 2 |
| #97×D101 | 2 |
| #442×C101 | 2 |
| #2943 | 101 |