Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
332 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 124 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×C17 | C22⋊C4 |
| commutator | C22 | C22×C8×C17 |
| Frattini, cosocle | C22×C4 | C23×C17 |
| socle | C22×C17 | C2×C22⋊C4 |
| prime radical | C22×D4×C17 | C4 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C23×C4×C17 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C17×C22⋊C8 | C2 | semidirect |
| 3. C17×#324 | C2 | semidirect |
| 4. C17×#323 | C2 | semidirect |
| 21. C2×D4×C17 | C8 | semidirect |
| 48. C23×C17 | C2×C8 | semidirect |
| 66. C2×C4×C17 | C2×C8 | semidirect |
| 69. #1459 | C17 | direct (N × H) |
| 92. C2×C22⋊C8 | C2×C17 | semidirect |
| 93. #324 | C2×C17 | semidirect |
| 94. #323 | C2×C17 | semidirect |
| 114. C17 | #1459 | direct (N × H) |
| 119. C2×D4 | C8×C17 | semidirect |
| 146. C23 | C2×C8×C17 | semidirect |
| 164. C2×C4 | C2×C8×C17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D4×C17 | 2 |
| C2×C17×C22⋊C8 | 2 |
| C17×#324 | 2 |
| C17×#323 | 2 |
| #1459 | 17 |