Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
456 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 175 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 |
|---|---|---|
| 3. #26041387 | C2 | semidirect |
| 4. #26041386 | C2 | semidirect |
| 5. #26041385 | C2 | semidirect |
| 6. C4×#15668439 | C2 | semidirect |
| 7. #26041371 | C2 | semidirect |
| 11. #441×C181 | C2 | semidirect |
| 15. Q16×D181 | C4 | semidirect |
| 108. C181 | #2950 | semidirect |
| 115. #441 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D181 | 2 |
| #26041755 | 2 |
| #26041387 | 2 |
| #26041386 | 2 |
| #26041385 | 2 |
| C4×#15668439 | 2 |
| #26041371 | 2 |
| #26041314 | 2 |
| #26041286 | 2 |
| #26041236 | 2 |
| #441×C181 | 2 |
| #2950 | 181 |