Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
250 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #120 |
| commutator, Frattini, cosocle | C42 | C23×C17 |
| prime radical | C17×#459 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C42×C17 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D4×Q8×C17 | C2 | semidirect |
| 2. C17×#486 | C2 | semidirect |
| 3. C17×#460 | C2 | semidirect |
| 5. C17×#332 | C2 | semidirect |
| 6. C17×Q8⋊C8 | C2 | semidirect |
| 7. C17×D4⋊C8 | C2 | semidirect |
| 57. Q8×C17 | D8 | semidirect |
| 64. D4×C17 | SD16 | semidirect |
| 78. #1627 | C17 | direct (N × H) |
| 95. D4×Q8 | C2×C17 | semidirect |
| 96. #486 | C2×C17 | semidirect |
| 97. #460 | C2×C17 | semidirect |
| 99. #332 | C2×C17 | semidirect |
| 100. Q8⋊C8 | C2×C17 | semidirect |
| 101. D4⋊C8 | C2×C17 | semidirect |
| 124. C17 | #1627 | direct (N × H) |
| 157. Q8 | D8×C17 | semidirect |
| 164. D4 | SD16×C17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Q8×C17 | 2 |
| C17×#486 | 2 |
| C17×#460 | 2 |
| C17×#459 | 2 |
| C17×#332 | 2 |
| C17×Q8⋊C8 | 2 |
| C17×D4⋊C8 | 2 |
| #1627 | 17 |