Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
432 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 145 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. #27212915 | C2 | semidirect |
| 4. #27212914 | C2 | semidirect |
| 5. #343×C211 | C2 | semidirect |
| 11. M16×D211 | C4 | semidirect |
| 31. #16809946 | C2×C4 | semidirect |
| 40. M16×C211 | C2×C4 | semidirect |
| 93. D211 | #343 | direct (N × H) |
| 94. C211 | C2×#343 | semidirect |
| 100. #343 | D211 | direct (N × H) |
| 131. M16 | C4×D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×D211 | 2 |
| C2×C4⋊C4×D211 | 2 |
| #27212915 | 2 |
| #27212914 | 2 |
| #343×C211 | 2 |
| C2×#343 | 211 |