Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
162 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 65 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. #26041106 | C2 | semidirect |
| 4. #26041083 | C2 | semidirect |
| 6. C4×#15668424 | C2 | semidirect |
| 7. C4×Q16×C181 | C2 | semidirect |
| 10. #19153759 | C4 | direct (N × H) |
| 27. #15668424 | C2×C4 | semidirect |
| 30. Q16×C181 | C2×C4 | semidirect |
| 59. C4×C181 | SD32 | semidirect |
| 67. C181 | C4×SD32 | semidirect |
| 70. C4×Q16 | D181 | semidirect |
| 92. Q16 | C4×D181 | semidirect |
| 128. C4 | #19153759 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153759 | 2 |
| C4×D1448 | 2 |
| #26041106 | 2 |
| #26041083 | 2 |
| #26041079 | 2 |
| C4×#15668424 | 2 |
| C4×Q16×C181 | 2 |
| C4×SD32 | 181 |