Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
368 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 77 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×#19153731 | C2 | semidirect |
| 2. #26041072 | C2 | direct (N × H) |
| 6. #19153731 | C22 | semidirect |
| 8. C22×D4×C181 | C4 | semidirect |
| 11. #127×C181 | C4 | semidirect |
| 13. C2×C42×C181 | C4 | semidirect |
| 28. C2×D4×C181 | C2×C4 | semidirect |
| 34. C42×C181 | C2×C4 | semidirect |
| 83. C2×C181 | #353 | semidirect |
| 85. C181 | C2×#353 | semidirect |
| 91. C22×D4 | Dic181 | semidirect |
| 94. #127 | Dic181 | semidirect |
| 97. C2×C42 | Dic181 | semidirect |
| 111. C2×D4 | C2×Dic181 | semidirect |
| 120. C42 | C2×Dic181 | semidirect |
| 169. C2 | #26041072 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153731 | 2 |
| #26041072 | 2 |
| C2×#127×C181 | 2 |
| C2×#353 | 181 |