Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
370 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 93 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×#19153743 | C2 | semidirect |
| 3. #26041283 | C2 | semidirect |
| 4. #26041180 | C2 | semidirect |
| 5. #26041048 | C2 | semidirect |
| 6. #26041038 | C2 | semidirect |
| 7. #520×C181 | C2 | semidirect |
| 10. #19153841 | C4 | semidirect |
| 34. C2×D724 | C2×C4 | semidirect |
| 41. #15668433 | C2×C4 | semidirect |
| 84. Q8×C181 | C22⋊C4 | semidirect |
| 88. D4×C181 | C22⋊C4 | semidirect |
| 132. C181 | #1883 | semidirect |
| 135. #520 | D181 | semidirect |
| 208. Q8 | #15668426 | semidirect |
| 216. D4 | #15668426 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153841 | 2 |
| C2×#19153743 | 2 |
| #26041283 | 2 |
| #26041180 | 2 |
| #26041048 | 2 |
| #26041038 | 2 |
| #520×C181 | 2 |
| #1883 | 181 |