Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
164 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 71 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×#19153755 | C2 | semidirect |
| 2. C22×#15668424 | C2 | semidirect |
| 4. #26041097 | C2 | semidirect |
| 5. #26041058 | C2 | semidirect |
| 6. #26041054 | C2 | semidirect |
| 7. C22⋊C16×C181 | C2 | semidirect |
| 32. #15668424 | D4 | semidirect |
| 59. C22×C181 | M32 | semidirect |
| 75. C181 | #2168 | semidirect |
| 82. C22⋊C16 | D181 | semidirect |
| 138. C22 | #19153755 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153755 | 2 |
| C22×#15668424 | 2 |
| C8×C22⋊D181 | 2 |
| #26041097 | 2 |
| #26041058 | 2 |
| #26041054 | 2 |
| C22⋊C16×C181 | 2 |
| #2168 | 181 |