Finite Group DatabasebetaFinite Group DatabasebetaOrder 22336.
202 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 63 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×C8×D349 | C2 | semidirect |
| 3. C4⋊C4×D349 | C2 | semidirect |
| 4. #26013561 | C2 | semidirect |
| 5. #26013560 | C2 | semidirect |
| 6. #26013559 | C2 | semidirect |
| 7. #102×C349 | C2 | semidirect |
| 12. D4×D349 | C4 | semidirect |
| 15. C2×#14584095 | C22 | semidirect |
| 17. C4⋊Dic349 | C22 | semidirect |
| 20. C2×C8×C349 | C22 | semidirect |
| 21. C4⋊C4×C349 | C22 | semidirect |
| 28. D1396 | C2×C4 | semidirect |
| 38. D4×C349 | C2×C4 | semidirect |
| 63. D349 | #102 | direct (N × H) |
| 64. C349 | C2×#102 | semidirect |
| 72. #102 | D349 | direct (N × H) |
| 83. C2×C8 | C2×D349 | semidirect |
| 86. C4⋊C4 | C2×D349 | semidirect |
| 97. D4 | C4×D349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×D349 | 2 |
| C2×C8×D349 | 2 |
| C4⋊C4×D349 | 2 |
| #26013561 | 2 |
| #26013560 | 2 |
| #26013559 | 2 |
| #102×C349 | 2 |
| C2×#102 | 349 |