Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
430 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 119 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. #20265725 | C2 | semidirect |
| 2. C4×#13108073 | C2 | semidirect |
| 3. #20265500 | C2 | semidirect |
| 4. #20265463 | C2 | semidirect |
| 5. #20265457 | C2 | semidirect |
| 6. #20265374 | C2 | semidirect |
| 7. #20265319 | C2 | semidirect |
| 8. #20265289 | C2 | semidirect |
| 9. #20265274 | C2 | semidirect |
| 10. #20265233 | C2 | semidirect |
| 11. #459×C101 | C2 | semidirect |
| 91. D4×C101 | #41 | semidirect |
| 114. Dic202 | #41 | semidirect |
| 145. C101 | #3115 | semidirect |
| 152. #459 | D101 | semidirect |
| 241. D4 | #13108073 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265725 | 2 |
| C4×#13108073 | 2 |
| #20265500 | 2 |
| #20265463 | 2 |
| #20265457 | 2 |
| #20265374 | 2 |
| #20265319 | 2 |
| #20265289 | 2 |
| #20265274 | 2 |
| #20265233 | 2 |
| #459×C101 | 2 |
| #3115 | 101 |