Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
360 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 360 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. #31826906 | C2 | direct (N × H) |
| 3. C2×#22583556 | C2 | semidirect |
| 4. C2×#22583553 | C2 | semidirect |
| 5. C2×#22583550 | C2 | semidirect |
| 6. C22×Q16×C283 | C2 | semidirect |
| 13. #22583556 | C22 | semidirect |
| 14. #22583553 | C22 | semidirect |
| 15. #22583550 | C22 | semidirect |
| 21. C2×Q16×C283 | C22 | semidirect |
| 80. C2×C283 | #510 | semidirect |
| 83. C283 | C2×#510 | semidirect |
| 86. C22×Q16 | D283 | semidirect |
| 99. C2×Q16 | C2×D283 | semidirect |
| 165. C2 | #31826906 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583632 | 2 |
| #31826906 | 2 |
| C2×#22583556 | 2 |
| C2×#22583553 | 2 |
| C2×#22583550 | 2 |
| C22×Q16×C283 | 2 |
| C2×#510 | 283 |