Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
180 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C211 | C2×D4 |
| commutator | C2×C4 | C22×C4×C211 |
| Frattini, cosocle | C42 | C23×C211 |
| socle | C22×C211 | C4×D4 |
| prime radical | C2×D8×C211 | C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C211 ◁ C4×C8×C211 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #436×C211 | C2 | semidirect |
| 3. #335×C211 | C2 | semidirect |
| 4. D4⋊C8×C211 | C2 | semidirect |
| 5. C82×C211 | C2 | semidirect |
| 42. C8×C211 | M16 | semidirect |
| 43. C8×C211 | D8 | semidirect |
| 58. C211 | #1589 | direct (N × H) |
| 59. #1589 | C211 | direct (N × H) |
| 61. #436 | C2×C211 | semidirect |
| 62. #335 | C2×C211 | semidirect |
| 63. D4⋊C8 | C2×C211 | semidirect |
| 64. C82 | C2×C211 | semidirect |
| 101. C8 | M16×C211 | semidirect |
| 102. C8 | D8×C211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D8×C211 | 2 |
| #436×C211 | 2 |
| #335×C211 | 2 |
| D4⋊C8×C211 | 2 |
| C82×C211 | 2 |
| #1589 | 211 |