Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
572 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 572 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×#15692285 | C2 | semidirect |
| 2. C2×#15692280 | C2 | semidirect |
| 3. C2×#15692243 | C2 | semidirect |
| 4. #20265569 | C2 | semidirect |
| 5. #20265564 | C2 | semidirect |
| 6. #20265559 | C2 | semidirect |
| 7. C4×#13108058 | C2 | semidirect |
| 8. #532×C101 | C2 | semidirect |
| 13. C2×#13108064 | C22 | semidirect |
| 14. C2×#13108062 | C22 | semidirect |
| 22. #15692166 | C22 | semidirect |
| 23. C4×#11717579 | C22 | semidirect |
| 25. C4⋊Q8×C101 | C22 | semidirect |
| 26. #127×C101 | C22 | semidirect |
| 27. #124×C101 | C22 | semidirect |
| 43. #13108058 | D4 | semidirect |
| 107. C101 | #3153 | semidirect |
| 110. #532 | D101 | semidirect |
| 126. C4⋊Q8 | C2×D101 | semidirect |
| 127. #127 | C2×D101 | semidirect |
| 131. #124 | 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×#15692280 | 2 |
| C2×#15692243 | 2 |
| #20265569 | 2 |
| #20265564 | 2 |
| #20265559 | 2 |
| C4×#13108058 | 2 |
| #532×C101 | 2 |
| #3153 | 101 |