Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
264 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 74 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. D101⋊#108 | C2 | semidirect |
| 2. C2×#15692323 | C2 | semidirect |
| 4. #20266056 | C2 | semidirect |
| 16. #15692263 | C4 | semidirect |
| 17. #15692262 | C4 | semidirect |
| 19. #15692261 | C4 | semidirect |
| 24. #131×C101 | C4 | semidirect |
| 113. C101 | #1815 | semidirect |
| 125. #131 | #87938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D101⋊#108 | 2 |
| C2×#15692323 | 2 |
| #20266168 | 2 |
| #20266056 | 2 |
| #131×D101 | 2 |
| #1815 | 101 |