Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
608 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 608 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 |
|---|---|---|
| 2. C2×C4×D724 | C2 | semidirect |
| 3. #26041392 | C2 | direct (N × H) |
| 4. C2×#19153748 | C2 | semidirect |
| 5. C2×#19153738 | C2 | semidirect |
| 6. C2×#97×C181 | C2 | semidirect |
| 9. C2×D1448 | C4 | semidirect |
| 12. C4×D724 | C22 | semidirect |
| 15. #19153748 | C22 | semidirect |
| 16. #19153738 | C22 | semidirect |
| 20. #97×C181 | C22 | semidirect |
| 24. C2×D724 | C2×C4 | semidirect |
| 29. D1448 | C2×C4 | semidirect |
| 36. C2×C8×C181 | C2×C4 | semidirect |
| 47. D724 | C22×C4 | semidirect |
| 59. C8×C181 | C22×C4 | semidirect |
| 72. C2×C181 | #442 | semidirect |
| 76. C181 | C2×#442 | semidirect |
| 83. C2×#97 | D181 | semidirect |
| 97. #97 | C2×D181 | semidirect |
| 110. C2×C8 | C4×D181 | semidirect |
| 136. C8 | C2×C4×D181 | semidirect |
| 150. C2 | #26041392 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1448 | 2 |
| C2×C4×D724 | 2 |
| #26041392 | 2 |
| C2×#19153748 | 2 |
| C2×#19153738 | 2 |
| C2×#97×C181 | 2 |
| C2×#442 | 181 |