Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
444 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 444 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×#15668436 | C2 | semidirect |
| 3. C2×#19153740 | C2 | semidirect |
| 4. C2×#19153736 | C2 | semidirect |
| 5. C2×C22⋊#13089678 | C2 | semidirect |
| 6. #26041041 | C2 | semidirect |
| 7. C2×C22⋊Q8×C181 | C2 | semidirect |
| 46. C2×#13089678 | D4 | semidirect |
| 56. C2×Q8×C181 | D4 | semidirect |
| 69. C4⋊C4×C181 | D4 | semidirect |
| 94. C23×C181 | SD16 | semidirect |
| 157. C181 | #2000 | semidirect |
| 160. C2×C22⋊Q8 | D181 | semidirect |
| 194. C2×Q8 | C22⋊D181 | semidirect |
| 226. C4⋊C4 | C22⋊D181 | semidirect |
| 242. C23 | #15668436 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668436 | 2 |
| C2×#19153790 | 2 |
| C2×#19153740 | 2 |
| C2×#19153736 | 2 |
| C2×C22⋊#13089678 | 2 |
| #26041041 | 2 |
| C2×C22⋊Q8×C181 | 2 |
| #2000 | 181 |