Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
456 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 175 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. #20265285 | C2 | semidirect |
| 4. #20265284 | C2 | semidirect |
| 5. #20265283 | C2 | semidirect |
| 6. C4×#13108064 | C2 | semidirect |
| 7. #20265269 | C2 | semidirect |
| 11. #441×C101 | C2 | semidirect |
| 15. Q16×D101 | C4 | semidirect |
| 109. C101 | #2950 | semidirect |
| 115. #441 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D101 | 2 |
| #20265653 | 2 |
| #20265285 | 2 |
| #20265284 | 2 |
| #20265283 | 2 |
| C4×#13108064 | 2 |
| #20265269 | 2 |
| #20265212 | 2 |
| #20265184 | 2 |
| #20265134 | 2 |
| #441×C101 | 2 |
| #2950 | 101 |