Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
492 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 221 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 |
|---|---|---|
| 1. #31771083 | C2 | semidirect |
| 3. #31770706 | C2 | semidirect |
| 4. SD16×Dic269 | C2 | semidirect |
| 5. #31770643 | C2 | semidirect |
| 6. #31770614 | C2 | semidirect |
| 8. #31770560 | C2 | semidirect |
| 12. Q8×Dic269 | C22 | semidirect |
| 20. #22575387 | C22 | semidirect |
| 21. #22575385 | C22 | semidirect |
| 22. #22575377 | C22 | semidirect |
| 24. #22575363 | C22 | semidirect |
| 25. C8×Dic269 | C22 | semidirect |
| 28. C2×SD16×C269 | C4 | semidirect |
| 50. C2×Q8×C269 | C2×C4 | semidirect |
| 58. SD16×C269 | C2×C4 | semidirect |
| 59. SD16×C269 | C2×C4 | semidirect |
| 60. C2×C8×C269 | C2×C4 | semidirect |
| 103. C269 | #2949 | semidirect |
| 116. C2×SD16 | Dic269 | semidirect |
| 139. C2×Q8 | C2×Dic269 | semidirect |
| 148. SD16 | C2×Dic269 | semidirect |
| 149. SD16 | C2×Dic269 | semidirect |
| 152. C2×C8 | C2×Dic269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771083 | 2 |
| #31771080 | 2 |
| #31770706 | 2 |
| SD16×Dic269 | 2 |
| #31770643 | 2 |
| #31770614 | 2 |
| #31770610 | 2 |
| #31770560 | 2 |
| C22×SD16×C269 | 2 |
| #2949 | 269 |