Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
544 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 205 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. #26041377 | C2 | direct (N × H) |
| 4. C2×#19153749 | C2 | semidirect |
| 5. C2×#19153740 | C2 | semidirect |
| 7. C2×#19153727 | C2 | semidirect |
| 8. C2×C4×Q8×C181 | C2 | semidirect |
| 11. C2×#15668436 | C4 | semidirect |
| 19. #19153749 | C22 | semidirect |
| 20. #19153740 | C22 | semidirect |
| 22. #19153727 | C22 | semidirect |
| 25. C4×Q8×C181 | C22 | semidirect |
| 38. #15668436 | C2×C4 | semidirect |
| 40. C2×#13089678 | C2×C4 | semidirect |
| 48. C2×Q8×C181 | C2×C4 | semidirect |
| 72. #13089678 | C22×C4 | semidirect |
| 76. Q8×C181 | C22×C4 | semidirect |
| 105. C2×C181 | #440 | semidirect |
| 110. C181 | C2×#440 | semidirect |
| 113. C2×C4×Q8 | D181 | semidirect |
| 128. C4×Q8 | C2×D181 | semidirect |
| 144. C2×Q8 | C4×D181 | semidirect |
| 179. Q8 | C2×C4×D181 | semidirect |
| 217. C2 | #26041377 | 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 |
| #26041377 | 2 |
| C2×#19153749 | 2 |
| C2×#19153740 | 2 |
| C2×#19153736 | 2 |
| C2×#19153727 | 2 |
| C2×C4×Q8×C181 | 2 |
| C2×#440 | 181 |