Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
490 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 490 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 |
|---|---|---|
| 1. C22×#13108061 | C2 | semidirect |
| 3. #20265655 | C2 | semidirect |
| 4. #20265401 | C2 | semidirect |
| 5. #20265375 | C2 | semidirect |
| 6. #20265205 | C2 | semidirect |
| 7. #20265183 | C2 | semidirect |
| 8. #20265173 | C2 | semidirect |
| 9. C2×#137×C101 | C2 | semidirect |
| 19. Q8×Dic101 | C22 | semidirect |
| 23. #15692184 | C22 | semidirect |
| 24. #15692179 | C22 | semidirect |
| 26. #15692176 | C22 | semidirect |
| 30. C2×Q16×C101 | C22 | semidirect |
| 31. C2×SD16×C101 | C22 | semidirect |
| 55. C2×Q8×C101 | D4 | semidirect |
| 117. C101 | #3043 | semidirect |
| 118. C2×#137 | D101 | semidirect |
| 131. C2×Q16 | C2×D101 | semidirect |
| 134. C2×SD16 | C2×D101 | semidirect |
| 155. C2×Q8 | C22⋊D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13108061 | 2 |
| #20265741 | 2 |
| #20265655 | 2 |
| #20265401 | 2 |
| #20265375 | 2 |
| #20265205 | 2 |
| #20265183 | 2 |
| #20265173 | 2 |
| C2×#137×C101 | 2 |
| #3043 | 101 |