Finite Group DatabasebetaFinite Group DatabasebetaOrder 22336.
122 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 55 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 |
|---|---|---|
| 3. #26013570 | C2 | semidirect |
| 4. #26013563 | C2 | semidirect |
| 6. C4×#14584095 | C2 | semidirect |
| 7. C4×Q8×C349 | C2 | semidirect |
| 10. #19150220 | C4 | direct (N × H) |
| 26. #14584095 | C2×C4 | semidirect |
| 28. Q8×C349 | C2×C4 | semidirect |
| 41. C4×C349 | SD16 | semidirect |
| 49. C349 | C4×SD16 | semidirect |
| 52. C4×Q8 | D349 | semidirect |
| 72. Q8 | C4×D349 | semidirect |
| 92. C4 | #19150220 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19150220 | 2 |
| C4×D1396 | 2 |
| #26013570 | 2 |
| #26013563 | 2 |
| #26013559 | 2 |
| C4×#14584095 | 2 |
| C4×Q8×C349 | 2 |
| C4×SD16 | 349 |