Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
284 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 108 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 | C2×C4 | C22×C4×C17 |
| Frattini, cosocle | C22×C4 | C23×C17 |
| socle | C22×C17 | C2×C22⋊C4 |
| prime radical | C17×#532 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C2×C42×C17 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C17×#431 | C2 | semidirect |
| 3. C4×C4⋊C4×C17 | C2 | semidirect |
| 4. C17×#327 | C2 | semidirect |
| 6. C17×C4⋊Q8 | C4 | semidirect |
| 7. C17×#127 | C4 | semidirect |
| 12. C4×D4×C17 | C4 | semidirect |
| 67. #1502 | C17 | direct (N × H) |
| 85. #431 | C2×C17 | semidirect |
| 86. C4×C4⋊C4 | C2×C17 | semidirect |
| 87. #327 | C2×C17 | semidirect |
| 95. C4⋊Q8 | C4×C17 | semidirect |
| 96. #127 | C4×C17 | semidirect |
| 101. C4×D4 | C4×C17 | semidirect |
| 109. C17 | #1502 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C17×#532 | 2 |
| C17×#431 | 2 |
| C4×C4⋊C4×C17 | 2 |
| C17×#327 | 2 |
| #1502 | 17 |