Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
812 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 812 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. C22×#13108073 | C2 | semidirect |
| 2. C22×#13108063 | C2 | semidirect |
| 3. C22×#13108059 | C2 | semidirect |
| 4. C2×#15692230 | C2 | semidirect |
| 5. #20265323 | C2 | direct (N × H) |
| 6. C2×#15692178 | C2 | semidirect |
| 7. C2×#15692167 | C2 | semidirect |
| 8. C2×#102×C101 | C2 | semidirect |
| 12. C2×#13108073 | C22 | semidirect |
| 20. C2×#13108063 | C22 | semidirect |
| 22. C2×#13108059 | C22 | semidirect |
| 25. #15692230 | C22 | semidirect |
| 27. #15692178 | C22 | semidirect |
| 28. #15692167 | C22 | semidirect |
| 32. #102×C101 | C22 | semidirect |
| 40. C2×Dic202 | D4 | semidirect |
| 66. C2×D4×C101 | D4 | semidirect |
| 89. D4×C101 | C2×D4 | semidirect |
| 111. Dic202 | C2×D4 | semidirect |
| 137. C2×C101 | #449 | semidirect |
| 144. C101 | C2×#449 | semidirect |
| 151. C2×#102 | D101 | semidirect |
| 175. #102 | C2×D101 | semidirect |
| 197. C2×D4 | D404 | semidirect |
| 241. D4 | C2×D404 | semidirect |
| 283. C2 | #20265323 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13108073 | 2 |
| C22×#13108063 | 2 |
| C22×#13108059 | 2 |
| C2×#15692230 | 2 |
| #20265323 | 2 |
| C2×#15692178 | 2 |
| C2×#15692167 | 2 |
| C2×#102×C101 | 2 |
| C2×#449 | 101 |