Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
394 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 394 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 |
|---|---|---|
| 1. C2×#15692288 | C2 | semidirect |
| 3. C2×#15692243 | C2 | semidirect |
| 4. C2×#15692183 | C2 | semidirect |
| 5. #20265185 | C2 | semidirect |
| 6. C2×#15692171 | C2 | semidirect |
| 7. #339×C101 | C2 | semidirect |
| 40. C2×Dic202 | D4 | semidirect |
| 62. M16×C101 | D4 | semidirect |
| 68. C42×C101 | D4 | semidirect |
| 132. C101 | #2004 | semidirect |
| 139. #339 | D101 | semidirect |
| 191. M16 | D404 | semidirect |
| 200. C42 | D404 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692288 | 2 |
| #20265746 | 2 |
| C2×#15692243 | 2 |
| C2×#15692183 | 2 |
| #20265185 | 2 |
| C2×#15692171 | 2 |
| #339×C101 | 2 |
| #2004 | 101 |