Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
408 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 109 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. C22×#15668433 | C2 | semidirect |
| 3. C2×#19153728 | C2 | semidirect |
| 4. #26041033 | C2 | semidirect |
| 5. C2×C22⋊C8×C181 | C2 | semidirect |
| 35. C2×#13089678 | D4 | semidirect |
| 55. C22×D181 | M16 | semidirect |
| 63. C2×Dic181 | M16 | semidirect |
| 113. C181 | #1870 | semidirect |
| 118. C2×C22⋊C8 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668433 | 2 |
| C2×C4×C22⋊D181 | 2 |
| C2×#19153728 | 2 |
| #26041033 | 2 |
| C2×C22⋊C8×C181 | 2 |
| #1870 | 181 |