Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
360 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 133 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. #24923710 | C2 | direct (N × H) |
| 3. C2×#19128778 | C2 | semidirect |
| 4. C2×#19128775 | C2 | semidirect |
| 5. C2×#19128772 | C2 | semidirect |
| 6. C22×Q16×C167 | C2 | semidirect |
| 13. #19128778 | C22 | semidirect |
| 14. #19128775 | C22 | semidirect |
| 15. #19128772 | C22 | semidirect |
| 21. C2×Q16×C167 | C22 | semidirect |
| 80. C2×C167 | #510 | semidirect |
| 83. C167 | C2×#510 | semidirect |
| 86. C22×Q16 | D167 | semidirect |
| 99. C2×Q16 | C2×D167 | semidirect |
| 165. C2 | #24923710 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128854 | 2 |
| #24923710 | 2 |
| C2×#19128778 | 2 |
| C2×#19128775 | 2 |
| C2×#19128772 | 2 |
| C22×Q16×C167 | 2 |
| C2×#510 | 167 |