Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
496 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 135 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×#15692285 | C2 | semidirect |
| 2. C2×M16×D101 | C2 | semidirect |
| 4. C2×#15692235 | C2 | semidirect |
| 5. #20265434 | C2 | semidirect |
| 6. #20265422 | C2 | semidirect |
| 7. #20265417 | C2 | semidirect |
| 8. #20265405 | C2 | semidirect |
| 9. #20265217 | C2 | semidirect |
| 10. #20265187 | C2 | semidirect |
| 11. #417×C101 | C2 | semidirect |
| 15. C2×#13108064 | C22 | semidirect |
| 16. C2×#13108062 | C22 | semidirect |
| 36. #15692188 | C22 | semidirect |
| 37. #15692186 | C22 | semidirect |
| 38. #15692180 | C22 | semidirect |
| 39. #15692180 | C22 | semidirect |
| 43. #103×C101 | C22 | semidirect |
| 44. #102×C101 | C22 | semidirect |
| 62. #13108058 | D4 | semidirect |
| 145. C2×D101 | #137 | semidirect |
| 164. C101 | #3056 | semidirect |
| 175. #417 | D101 | semidirect |
| 207. #103 | C2×D101 | semidirect |
| 208. #102 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692285 | 2 |
| C2×M16×D101 | 2 |
| #20265684 | 2 |
| C2×#15692235 | 2 |
| #20265434 | 2 |
| #20265422 | 2 |
| #20265417 | 2 |
| #20265405 | 2 |
| #20265217 | 2 |
| #20265187 | 2 |
| #417×C101 | 2 |
| #3056 | 101 |