Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
688 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 152 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. #20266129 | C2 | semidirect |
| 2. #20266127 | C2 | semidirect |
| 3. #20266125 | C2 | semidirect |
| 4. #20266118 | C2 | semidirect |
| 6. C23×#87938 | C22 | semidirect |
| 7. C2×C4⋊#87938 | C22 | semidirect |
| 10. C2×C22⋊#87938 | C22 | semidirect |
| 11. C2×C4×#87938 | C22 | semidirect |
| 12. (C2×#87938)⋊C4 | C22 | semidirect |
| 15. #15692225 | C4 | semidirect |
| 16. #15692224 | C4 | semidirect |
| 17. #15692223 | C4 | semidirect |
| 19. #120×C101 | C4 | semidirect |
| 30. C23×D101 | C2×C4 | semidirect |
| 39. C22⋊Dic101 | C2×C4 | semidirect |
| 40. #13108051 | C2×C4 | semidirect |
| 41. C24×C101 | C2×C4 | semidirect |
| 43. C22⋊C4×C101 | C2×C4 | semidirect |
| 101. C101 | #2375 | semidirect |
| 113. #120 | #87938 | semidirect |
| 126. C24 | C2×#87938 | semidirect |
| 143. C22⋊C4 | C2×#87938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20266129 | 2 |
| #20266127 | 2 |
| #20266125 | 2 |
| #20266118 | 2 |
| #120×D101 | 2 |
| #2375 | 101 |