Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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×#15668432 | C2 | semidirect |
| 2. #26041786 | C2 | semidirect |
| 3. #26041534 | C2 | semidirect |
| 4. #26041529 | C2 | semidirect |
| 5. #26041522 | C2 | semidirect |
| 6. #26041317 | C2 | semidirect |
| 7. #26041275 | C2 | semidirect |
| 8. C2×#135×C181 | C2 | semidirect |
| 20. #19153750 | C22 | semidirect |
| 21. #19153748 | C22 | semidirect |
| 22. #19153740 | C22 | semidirect |
| 23. #19153737 | C22 | semidirect |
| 26. C2×Q16×C181 | C22 | semidirect |
| 27. C2×SD16×C181 | C22 | semidirect |
| 28. C2×D8×C181 | C22 | semidirect |
| 57. C2×C8×C181 | D4 | semidirect |
| 105. C181 | #3054 | semidirect |
| 107. C2×#135 | D181 | semidirect |
| 118. C2×Q16 | C2×D181 | semidirect |
| 119. C2×SD16 | C2×D181 | semidirect |
| 120. C2×D8 | C2×D181 | semidirect |
| 157. C2×C8 | C22⋊D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668432 | 2 |
| #26041786 | 2 |
| #26041534 | 2 |
| #26041529 | 2 |
| #26041522 | 2 |
| #26041317 | 2 |
| #26041275 | 2 |
| C2×#135×C181 | 2 |
| #3054 | 181 |