Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
732 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 165 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×#15692280 | C2 | semidirect |
| 2. C22×#13108061 | C2 | semidirect |
| 3. #20265741 | C2 | semidirect |
| 4. #20265322 | C2 | semidirect |
| 5. #20265316 | C2 | semidirect |
| 6. #20265186 | C2 | semidirect |
| 7. #20265173 | C2 | semidirect |
| 8. #20265144 | C2 | semidirect |
| 9. C2×2−1+4×C101 | C2 | semidirect |
| 23. #15692179 | C22 | semidirect |
| 24. #15692179 | C22 | semidirect |
| 25. #15692176 | C22 | semidirect |
| 26. C22⋊#11717579 | C22 | semidirect |
| 33. C2×#41×C101 | C22 | semidirect |
| 36. C22×Q8×C101 | C22 | semidirect |
| 61. #41×C101 | D4 | semidirect |
| 69. C2×Q8×C101 | D4 | semidirect |
| 146. C101 | #3010 | semidirect |
| 147. C2×2−1+4 | D101 | semidirect |
| 162. C2×#41 | C2×D101 | semidirect |
| 165. C22×Q8 | C2×D101 | semidirect |
| 191. #41 | C22⋊D101 | semidirect |
| 199. C2×Q8 | C22⋊D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692280 | 2 |
| C22×#13108061 | 2 |
| #20265741 | 2 |
| #20265322 | 2 |
| #20265316 | 2 |
| #20265186 | 2 |
| #20265173 | 2 |
| #20265144 | 2 |
| C2×2−1+4×C101 | 2 |
| #3010 | 101 |