Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
792 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 173 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. C22×Q8×D101 | C2 | semidirect |
| 2. C22×#13108063 | C2 | semidirect |
| 3. C22×#13108061 | C2 | semidirect |
| 5. #20265317 | C2 | direct (N × H) |
| 6. C2×#15692178 | C2 | semidirect |
| 7. C2×#15692167 | C2 | semidirect |
| 8. C2×#103×C101 | C2 | semidirect |
| 14. C2×Q8×D101 | C22 | semidirect |
| 20. C2×#13108063 | C22 | semidirect |
| 22. C2×#13108061 | C22 | semidirect |
| 27. #15692178 | C22 | semidirect |
| 28. #15692167 | C22 | semidirect |
| 32. #103×C101 | C22 | semidirect |
| 39. C2×Dic202 | D4 | semidirect |
| 65. C2×Q8×C101 | D4 | semidirect |
| 81. C22×D101 | SD16 | semidirect |
| 85. Q8×C101 | C2×D4 | semidirect |
| 109. Dic202 | C2×D4 | semidirect |
| 123. C2×D101 | C2×SD16 | semidirect |
| 131. C2×C101 | #448 | semidirect |
| 138. C101 | C2×#448 | semidirect |
| 145. C2×#103 | D101 | semidirect |
| 169. #103 | C2×D101 | semidirect |
| 184. C2×Q8 | D404 | semidirect |
| 227. Q8 | C2×D404 | semidirect |
| 271. C2 | #20265317 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D101 | 2 |
| C22×#13108063 | 2 |
| C22×#13108061 | 2 |
| C2×#15692230 | 2 |
| #20265317 | 2 |
| C2×#15692178 | 2 |
| C2×#15692167 | 2 |
| C2×#103×C101 | 2 |
| C2×#448 | 101 |