Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
754 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 754 conjugacy classes of subgroups — too many to draw. Only its 153 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. C2×#15692286 | C2 | semidirect |
| 3. #20265337 | C2 | semidirect |
| 4. #20265332 | C2 | semidirect |
| 5. #20265327 | C2 | semidirect |
| 6. #20265176 | C2 | semidirect |
| 7. #20265141 | C2 | semidirect |
| 8. C2×C22⋊Q8×C101 | C2 | semidirect |
| 19. C2×#13108064 | C22 | semidirect |
| 20. C2×#13108061 | C22 | semidirect |
| 21. C2×#13108058 | C22 | semidirect |
| 22. #15692178 | C22 | semidirect |
| 23. #15692175 | C22 | semidirect |
| 25. C22⋊#11717579 | C22 | semidirect |
| 26. C22×Q8×C101 | C22 | semidirect |
| 31. C22⋊Q8×C101 | C22 | semidirect |
| 33. C2×C4⋊C4×C101 | C22 | semidirect |
| 126. C22×C101 | #137 | semidirect |
| 147. C101 | #3007 | semidirect |
| 150. C2×C22⋊Q8 | D101 | semidirect |
| 162. C22×Q8 | C2×D101 | semidirect |
| 174. C22⋊Q8 | C2×D101 | semidirect |
| 176. C2×C4⋊C4 | C2×D101 | semidirect |
| 277. C22 | #15692286 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13108074 | 2 |
| C2×#15692286 | 2 |
| #20265337 | 2 |
| #20265332 | 2 |
| #20265327 | 2 |
| #20265176 | 2 |
| #20265141 | 2 |
| C2×C22⋊Q8×C101 | 2 |
| #3007 | 101 |