Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 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 |
|---|---|---|
| 3. #20265517 | C2 | semidirect |
| 4. #20265516 | C2 | semidirect |
| 5. #20265511 | C2 | semidirect |
| 6. #20265506 | C2 | semidirect |
| 7. #20265217 | C2 | semidirect |
| 8. #20265215 | C2 | semidirect |
| 9. #20265186 | C2 | semidirect |
| 11. C2×#103×C101 | C2 | semidirect |
| 127. C101 | #3097 | semidirect |
| 137. C2×#103 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265751 | 2 |
| #20265658 | 2 |
| #20265517 | 2 |
| #20265516 | 2 |
| #20265511 | 2 |
| #20265506 | 2 |
| #20265217 | 2 |
| #20265215 | 2 |
| #20265186 | 2 |
| #20265143 | 2 |
| C2×#103×C101 | 2 |
| #3097 | 101 |