Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
324 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 70 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. C2×#15692343 | C2 | semidirect |
| 2. C2×#15692320 | C2 | semidirect |
| 3. C2×#15692320 | C2 | semidirect |
| 4. #20266152 | C2 | semidirect |
| 5. #20266053 | C2 | semidirect |
| 6. (C2×#87938)⋊C8 | C2 | semidirect |
| 24. C2×#13108061 | C4 | semidirect |
| 25. C2×#13108061 | C4 | semidirect |
| 26. C2×D808 | C4 | semidirect |
| 28. C2×Q16×C101 | C4 | semidirect |
| 131. C101 | #1876 | semidirect |
| 143. C2×Q16 | #87938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692343 | 2 |
| C2×#15692320 | 2 |
| #20266152 | 2 |
| #20266053 | 2 |
| (C2×#87938)⋊C8 | 2 |
| C2×#15692278 | 2 |
| #1876 | 101 |