Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
380 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 141 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. #20265587 | C2 | semidirect |
| 4. #20265586 | C2 | semidirect |
| 5. #20265583 | C2 | semidirect |
| 6. #20265581 | C2 | semidirect |
| 7. #20265574 | C2 | semidirect |
| 11. #501×C101 | C2 | semidirect |
| 52. #13108057 | Q8 | semidirect |
| 102. C8×C101 | C2×Q8 | semidirect |
| 103. #11717579 | C2×Q8 | semidirect |
| 125. C101 | #3165 | semidirect |
| 131. #501 | D101 | semidirect |
| 228. C8 | Q8×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265733 | 2 |
| C4⋊Q8×D101 | 2 |
| #20265587 | 2 |
| #20265586 | 2 |
| #20265583 | 2 |
| #20265581 | 2 |
| #20265574 | 2 |
| #20265218 | 2 |
| #20265216 | 2 |
| #20265129 | 2 |
| #501×C101 | 2 |
| #3165 | 101 |