Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
392 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 173 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. #20265239 | C2 | semidirect |
| 3. #20265236 | C2 | semidirect |
| 4. #20265200 | C2 | semidirect |
| 6. C4×#13108058 | C2 | semidirect |
| 7. C4×M16×C101 | C2 | semidirect |
| 16. #15692184 | C22 | semidirect |
| 18. #15692166 | C22 | semidirect |
| 19. C4×#11717579 | C22 | semidirect |
| 22. #97×C101 | C22 | semidirect |
| 23. C4×C8×C101 | C22 | semidirect |
| 80. C101 | #2921 | semidirect |
| 87. C4×M16 | D101 | semidirect |
| 101. #97 | C2×D101 | semidirect |
| 103. C4×C8 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692212 | 2 |
| #20265239 | 2 |
| #20265236 | 2 |
| #20265200 | 2 |
| #20265140 | 2 |
| C4×#13108058 | 2 |
| C4×M16×C101 | 2 |
| #2921 | 101 |