Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 149 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×#15692280 | C2 | semidirect |
| 2. C22×D808 | C2 | semidirect |
| 3. #20265741 | C2 | semidirect |
| 4. #20265563 | C2 | semidirect |
| 5. #20265562 | C2 | semidirect |
| 6. #20265552 | C2 | semidirect |
| 7. #20265132 | C2 | semidirect |
| 8. C2×#135×C101 | C2 | semidirect |
| 11. C2×#13108061 | C22 | semidirect |
| 15. C2×#13108059 | C22 | semidirect |
| 17. #15692251 | C22 | semidirect |
| 18. #15692244 | C22 | semidirect |
| 22. #15692165 | C22 | semidirect |
| 23. C8×Dic101 | C22 | semidirect |
| 26. C2×Q16×C101 | C22 | semidirect |
| 27. C2×SD16×C101 | C22 | semidirect |
| 28. C2×D8×C101 | C22 | semidirect |
| 40. #13108058 | D4 | semidirect |
| 56. C2×C8×C101 | D4 | semidirect |
| 102. C101 | #3155 | semidirect |
| 104. C2×#135 | D101 | semidirect |
| 115. C2×Q16 | C2×D101 | semidirect |
| 117. C2×SD16 | C2×D101 | semidirect |
| 122. C2×D8 | C2×D101 | semidirect |
| 154. C2×C8 | C22⋊D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692280 | 2 |
| C22×D808 | 2 |
| #20265741 | 2 |
| #20265563 | 2 |
| #20265562 | 2 |
| #20265552 | 2 |
| #20265132 | 2 |
| C2×#135×C101 | 2 |
| #3155 | 101 |