Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
382 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 125 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. #20265543 | C2 | semidirect |
| 3. #20265525 | C2 | semidirect |
| 4. #20265474 | C2 | semidirect |
| 5. #20265454 | C2 | semidirect |
| 6. #20265377 | C2 | semidirect |
| 7. #20265377 | C2 | semidirect |
| 8. #20265308 | C2 | semidirect |
| 9. #20265275 | C2 | semidirect |
| 10. C4×#13108061 | C2 | semidirect |
| 11. #557×C101 | C2 | semidirect |
| 79. Q8×C101 | #41 | semidirect |
| 125. C101 | #3368 | semidirect |
| 126. #557 | D101 | semidirect |
| 204. Q8 | #13108075 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265849 | 2 |
| #20265543 | 2 |
| #20265525 | 2 |
| #20265474 | 2 |
| #20265454 | 2 |
| #20265377 | 2 |
| #20265308 | 2 |
| #20265275 | 2 |
| C4×#13108061 | 2 |
| #557×C101 | 2 |
| #3368 | 101 |