Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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×#15692244 | C2 | semidirect |
| 3. #41×Dic101 | C2 | semidirect |
| 4. #20265401 | C2 | semidirect |
| 5. #20265394 | C2 | semidirect |
| 6. #20265200 | C2 | semidirect |
| 7. #20265186 | C2 | semidirect |
| 8. #20265183 | C2 | semidirect |
| 9. C2×#137×C101 | C2 | semidirect |
| 18. Q8×Dic101 | C22 | semidirect |
| 20. D4×Dic101 | C22 | semidirect |
| 26. #15692184 | C22 | semidirect |
| 27. #15692179 | C22 | semidirect |
| 32. C2×Q16×C101 | C22 | semidirect |
| 33. C2×SD16×C101 | C22 | semidirect |
| 126. C101 | #3040 | semidirect |
| 127. C2×#137 | D101 | semidirect |
| 141. C2×Q16 | C2×D101 | semidirect |
| 143. C2×SD16 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692280 | 2 |
| C2×#15692244 | 2 |
| #41×Dic101 | 2 |
| #20265401 | 2 |
| #20265394 | 2 |
| #20265200 | 2 |
| #20265186 | 2 |
| #20265183 | 2 |
| C2×#137×C101 | 2 |
| #3040 | 101 |