Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
360 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 129 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. #24924074 | C2 | semidirect |
| 2. #24923710 | C2 | semidirect |
| 3. #24923704 | C2 | semidirect |
| 4. #24923699 | C2 | semidirect |
| 5. C2×#19128775 | C2 | semidirect |
| 6. #24923686 | C2 | semidirect |
| 7. #578×C167 | C2 | semidirect |
| 12. #19128778 | C22 | semidirect |
| 13. #19128776 | C22 | semidirect |
| 14. #19128775 | C22 | semidirect |
| 15. #19128775 | C22 | semidirect |
| 16. #19128773 | C22 | semidirect |
| 17. #19128772 | C22 | semidirect |
| 18. C2×C167⋊C16 | C22 | semidirect |
| 21. #135×C167 | C22 | semidirect |
| 22. C2×Q16×C167 | C22 | semidirect |
| 74. C167 | #3416 | semidirect |
| 76. #578 | D167 | semidirect |
| 88. #135 | C2×D167 | semidirect |
| 89. C2×Q16 | C2×D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24924074 | 2 |
| #24923710 | 2 |
| #24923704 | 2 |
| #24923699 | 2 |
| C2×#19128775 | 2 |
| #24923686 | 2 |
| #578×C167 | 2 |
| #3416 | 167 |