Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
424 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 121 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. C4×Q8×D101 | C2 | semidirect |
| 3. #20265489 | C2 | semidirect |
| 4. #20265473 | C2 | semidirect |
| 5. #20265472 | C2 | semidirect |
| 6. #20265374 | C2 | semidirect |
| 7. #20265314 | C2 | semidirect |
| 8. #20265278 | C2 | semidirect |
| 9. #20265274 | C2 | semidirect |
| 10. #20265233 | C2 | semidirect |
| 11. #460×C101 | C2 | semidirect |
| 86. Q8×C101 | #41 | semidirect |
| 113. Dic202 | #41 | semidirect |
| 141. C101 | #3112 | semidirect |
| 148. #460 | D101 | semidirect |
| 231. Q8 | #13108073 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265725 | 2 |
| C4×Q8×D101 | 2 |
| #20265489 | 2 |
| #20265473 | 2 |
| #20265472 | 2 |
| #20265374 | 2 |
| #20265314 | 2 |
| #20265278 | 2 |
| #20265274 | 2 |
| #20265233 | 2 |
| #460×C101 | 2 |
| #3112 | 101 |