Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
532 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 149 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×#19128863 | C2 | semidirect |
| 3. #24923843 | C2 | semidirect |
| 4. #24923662 | C2 | semidirect |
| 5. #24923654 | C2 | semidirect |
| 6. #24923647 | C2 | semidirect |
| 7. #24923224 | C2 | semidirect |
| 8. C22×Q16×C167 | C2 | semidirect |
| 96. C167 | #3156 | semidirect |
| 100. C22×Q16 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128863 | 2 |
| C2×#19128854 | 2 |
| #24923843 | 2 |
| #24923662 | 2 |
| #24923654 | 2 |
| #24923647 | 2 |
| #24923224 | 2 |
| C22×Q16×C167 | 2 |
| #3156 | 167 |