Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
216 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 47 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×#19153759 | C2 | semidirect |
| 3. #26041551 | C2 | semidirect |
| 4. #26041093 | C2 | semidirect |
| 5. #26041086 | C2 | semidirect |
| 6. #26041064 | C2 | semidirect |
| 7. #510×C181 | C2 | semidirect |
| 17. C2×#15668424 | C22 | semidirect |
| 18. #19153752 | C22 | semidirect |
| 21. C2×Q16×C181 | C22 | semidirect |
| 24. M32×C181 | C22 | semidirect |
| 91. C181 | #2194 | semidirect |
| 94. #510 | D181 | semidirect |
| 106. C2×Q16 | C2×D181 | semidirect |
| 113. M32 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042081 | 2 |
| C2×#19153759 | 2 |
| #26041551 | 2 |
| #26041093 | 2 |
| #26041086 | 2 |
| #26041064 | 2 |
| #510×C181 | 2 |
| #2194 | 181 |