Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
544 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 173 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 |
|---|---|---|
| 3. #26041481 | C2 | direct (N × H) |
| 4. C2×C4⋊#13089678 | C2 | semidirect |
| 5. C2×#19153740 | C2 | semidirect |
| 6. C2×C4⋊Q8×C181 | C2 | semidirect |
| 16. C4⋊#13089678 | C22 | semidirect |
| 17. #19153740 | C22 | semidirect |
| 20. C4⋊Q8×C181 | C22 | semidirect |
| 68. C2×C4×C181 | SD16 | semidirect |
| 86. C4×C181 | C2×SD16 | semidirect |
| 90. C2×C181 | #461 | semidirect |
| 95. C181 | C2×#461 | semidirect |
| 98. C2×C4⋊Q8 | D181 | semidirect |
| 110. C4⋊Q8 | C2×D181 | semidirect |
| 163. C2×C4 | #15668436 | semidirect |
| 183. C4 | C2×#15668436 | semidirect |
| 187. C2 | #26041481 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668436 | 2 |
| C2×C4×D724 | 2 |
| #26041481 | 2 |
| C2×C4⋊#13089678 | 2 |
| C2×#19153740 | 2 |
| C2×C4⋊Q8×C181 | 2 |
| C2×#461 | 181 |