Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
7118 conjugacy classes of subgroups; only the 1459 normal subgroups are shown.
This group has 7118 conjugacy classes of subgroups — too many to draw. Only its 1459 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. C2×#11762720 | C2 | direct (N × H) |
| 3. C22×#10587502 | C2 | semidirect |
| 4. C24×Q8×C17 | C2 | semidirect |
| 9. #11762720 | C22 | direct (N × H) |
| 10. C2×#10587502 | C22 | semidirect |
| 12. C23×Q8×C17 | C22 | semidirect |
| 17. C24×D17 | Q8 | semidirect |
| 21. C22×Q8×C17 | C23 | semidirect |
| 30. #10587502 | C23 | semidirect |
| 40. C23×D17 | C2×Q8 | semidirect |
| 67. C22×D17 | C22×Q8 | semidirect |
| 75. C24×Q8 | D17 | semidirect |
| 79. C22×C17 | #393 | semidirect |
| 94. C23×Q8 | C2×D17 | semidirect |
| 101. C2×C17 | C2×#393 | semidirect |
| 113. C22×Q8 | C22×D17 | semidirect |
| 123. C17 | C22×#393 | semidirect |
| 171. C22 | #11762720 | direct (N × H) |
| 181. C2 | C2×#11762720 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#63227 | 2 |
| C2×#11762720 | 2 |
| C22×#10587502 | 2 |
| C24×Q8×C17 | 2 |
| C22×#393 | 17 |