Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
240 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 4. #20264924 | C2 | semidirect |
| 5. #20264923 | C2 | semidirect |
| 6. #20264922 | C2 | semidirect |
| 7. #332×C101 | C2 | semidirect |
| 92. C101 | #1546 | semidirect |
| 99. #332 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D101 | 2 |
| #20265229 | 2 |
| #20265199 | 2 |
| #20264924 | 2 |
| #20264923 | 2 |
| #20264922 | 2 |
| #332×C101 | 2 |
| #1546 | 101 |