Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
174 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 81 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×C16×D181 | C2 | semidirect |
| 3. #26041097 | C2 | semidirect |
| 4. C22⋊#15668424 | C2 | semidirect |
| 5. #26041058 | C2 | semidirect |
| 6. C16×Dic181 | C2 | semidirect |
| 7. C22×C16×C181 | C2 | semidirect |
| 39. C16×C181 | D4 | semidirect |
| 41. C22⋊D181 | C16 | direct (N × H) |
| 59. C22×C181 | C2×C16 | semidirect |
| 63. C2×D181 | C2×C16 | semidirect |
| 69. Dic181 | C2×C16 | semidirect |
| 75. C181 | D4×C16 | semidirect |
| 78. C22×C16 | D181 | semidirect |
| 115. C16 | C22⋊D181 | direct (N × H) |
| 138. C22 | C16×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C16×D181 | 2 |
| C8×C22⋊D181 | 2 |
| #26041097 | 2 |
| C22⋊#15668424 | 2 |
| #26041058 | 2 |
| C16×Dic181 | 2 |
| C22×C16×C181 | 2 |
| D4×C16 | 181 |