Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
284 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 66 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. #20266187 | C2 | semidirect |
| 2. #20266176 | C2 | semidirect |
| 3. #20266158 | C2 | semidirect |
| 4. #20266140 | C2 | semidirect |
| 20. C2×#13108061 | C4 | semidirect |
| 21. C2×D808 | C4 | semidirect |
| 23. C2×Q16×C101 | C4 | semidirect |
| 97. C101 | #1976 | semidirect |
| 108. C2×Q16 | #87938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20266187 | 2 |
| #20266176 | 2 |
| #20266158 | 2 |
| #20266140 | 2 |
| C2×#15692278 | 2 |
| #1976 | 101 |