Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
456 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 173 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. #26041174 | C2 | semidirect |
| 4. #26041160 | C2 | semidirect |
| 6. #26041147 | C2 | semidirect |
| 7. #384×C181 | C2 | semidirect |
| 9. #19153810 | C4 | semidirect |
| 28. #15668428 | C2×C4 | semidirect |
| 37. C42×C181 | C2×C4 | semidirect |
| 72. C181 | #2383 | semidirect |
| 79. #384 | D181 | semidirect |
| 110. C42 | C4×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153810 | 2 |
| #26041174 | 2 |
| #26041169 | 2 |
| #26041160 | 2 |
| #26041150 | 2 |
| #26041147 | 2 |
| #384×C181 | 2 |
| #2383 | 181 |