Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
424 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 133 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. #26041592 | C2 | semidirect |
| 3. #26041574 | C2 | semidirect |
| 4. #26041479 | C2 | semidirect |
| 5. #26041418 | C2 | semidirect |
| 6. #26041377 | C2 | semidirect |
| 7. #26041336 | C2 | semidirect |
| 8. C2×C4×Q8×C181 | C2 | semidirect |
| 76. Q8×C181 | #41 | semidirect |
| 111. C181 | #3112 | semidirect |
| 114. C2×C4×Q8 | D181 | semidirect |
| 181. Q8 | #15668449 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041829 | 2 |
| #26041592 | 2 |
| #26041574 | 2 |
| #26041479 | 2 |
| #26041418 | 2 |
| #26041377 | 2 |
| #26041336 | 2 |
| C2×C4×Q8×C181 | 2 |
| #3112 | 181 |