Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
332 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 2. #20265645 | C2 | semidirect |
| 3. #20265195 | C2 | semidirect |
| 4. C2×#15692182 | C2 | semidirect |
| 5. #20264947 | C2 | semidirect |
| 6. #20264936 | C2 | semidirect |
| 7. #410×C101 | C2 | semidirect |
| 9. #15692286 | C4 | semidirect |
| 11. #15692281 | C4 | semidirect |
| 46. #13108058 | C2×C4 | semidirect |
| 59. C2×Q8×C101 | C2×C4 | semidirect |
| 61. C2×D4×C101 | C2×C4 | semidirect |
| 130. C101 | #1906 | semidirect |
| 135. #410 | D101 | semidirect |
| 168. C2×Q8 | C4×D101 | semidirect |
| 172. C2×D4 | C4×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265975 | 2 |
| #20265645 | 2 |
| #20265195 | 2 |
| C2×#15692182 | 2 |
| #20264947 | 2 |
| #20264936 | 2 |
| #410×C101 | 2 |
| #1906 | 101 |