Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
840 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 205 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. C2×#22576136 | C2 | semidirect |
| 3. #31773816 | C2 | semidirect |
| 4. #31773808 | C2 | semidirect |
| 5. #31773804 | C2 | semidirect |
| 7. #31773770 | C2 | semidirect |
| 8. #31773757 | C2 | semidirect |
| 9. C23×Q8×C271 | C2 | semidirect |
| 34. C2×C22⋊D271 | Q8 | semidirect |
| 55. C2×Q8×C271 | D4 | semidirect |
| 67. C22×D271 | C2×Q8 | semidirect |
| 78. C2×Dic271 | C2×Q8 | semidirect |
| 101. C22×C271 | C22⋊Q8 | semidirect |
| 126. C271 | #2409 | semidirect |
| 128. C23×Q8 | D271 | semidirect |
| 165. C2×Q8 | C22⋊D271 | semidirect |
| 233. C22 | #22576136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576136 | 2 |
| C2×C4×C22⋊D271 | 2 |
| #31773816 | 2 |
| #31773808 | 2 |
| #31773804 | 2 |
| #31773776 | 2 |
| #31773770 | 2 |
| #31773757 | 2 |
| C23×Q8×C271 | 2 |
| #2409 | 271 |