Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
174 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 55 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. C2×#15692196 | C2 | semidirect |
| 2. C22×#13108049 | C2 | semidirect |
| 3. #20265413 | C2 | semidirect |
| 4. #20265002 | C2 | semidirect |
| 5. #20264978 | C2 | semidirect |
| 6. #20264977 | C2 | semidirect |
| 7. #466×C101 | C2 | semidirect |
| 28. #13108049 | D4 | semidirect |
| 63. C22×C101 | D16 | semidirect |
| 80. C101 | #2215 | semidirect |
| 84. #466 | D101 | semidirect |
| 146. C22 | #15692196 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692196 | 2 |
| C22×#13108049 | 2 |
| #20265413 | 2 |
| #20265002 | 2 |
| #20264978 | 2 |
| #20264977 | 2 |
| #466×C101 | 2 |
| #2215 | 101 |