Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
496 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 95 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×#15668434 | C2 | semidirect |
| 2. C2×#19153790 | C2 | semidirect |
| 3. C2×#19153737 | C2 | semidirect |
| 4. C2×#19153736 | C2 | semidirect |
| 5. C2×C22⋊#13089678 | C2 | semidirect |
| 6. #26041041 | C2 | semidirect |
| 7. C2×#121×C181 | C2 | semidirect |
| 35. C2×D724 | D4 | semidirect |
| 46. C2×#13089678 | D4 | semidirect |
| 48. C4⋊Dic181 | D4 | semidirect |
| 60. C2×D4×C181 | D4 | semidirect |
| 71. C4⋊C4×C181 | D4 | semidirect |
| 103. C23×C181 | D8 | semidirect |
| 171. C181 | #1999 | semidirect |
| 175. C2×#121 | D181 | semidirect |
| 221. C2×D4 | C22⋊D181 | semidirect |
| 242. C4⋊C4 | C22⋊D181 | semidirect |
| 265. C23 | #15668434 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668434 | 2 |
| C2×#19153790 | 2 |
| C2×#19153737 | 2 |
| C2×#19153736 | 2 |
| C2×C22⋊#13089678 | 2 |
| #26041041 | 2 |
| C2×#121×C181 | 2 |
| #1999 | 181 |