Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
760 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 165 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 |
|---|---|---|
| 2. C22×#14558994 | C2 | semidirect |
| 3. C22×#14558991 | C2 | semidirect |
| 4. #23752372 | C2 | direct (N × H) |
| 5. C2×#18012662 | C2 | semidirect |
| 6. C2×#18012659 | C2 | semidirect |
| 7. C2×C22⋊(C151⋊C8) | C2 | semidirect |
| 8. C2×C22⋊Q8×C151 | C2 | semidirect |
| 18. C2×#14558994 | C22 | semidirect |
| 20. C2×#14558991 | C22 | semidirect |
| 23. #18012662 | C22 | semidirect |
| 24. #18012659 | C22 | semidirect |
| 25. C22⋊(C151⋊C8) | C22 | semidirect |
| 29. C22⋊Q8×C151 | C22 | semidirect |
| 130. C2×C151 | #452 | semidirect |
| 135. C151 | C2×#452 | semidirect |
| 140. C2×C22⋊Q8 | D151 | semidirect |
| 162. C22⋊Q8 | C2×D151 | semidirect |
| 267. C2 | #23752372 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14559004 | 2 |
| C22×#14558994 | 2 |
| C22×#14558991 | 2 |
| #23752372 | 2 |
| C2×#18012662 | 2 |
| C2×#18012659 | 2 |
| C2×C22⋊(C151⋊C8) | 2 |
| C2×C22⋊Q8×C151 | 2 |
| C2×#452 | 151 |